BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Colva Roney-Dougal (The University of St Andrews)
DTSTART:20201008T150000Z
DTEND:20201008T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/1
DESCRIPTION:Title: Finite simple groups and complexity class NP\nby Colva Roney-Dou
gal (The University of St Andrews) as part of GOThIC - Ischia Online Group
Theory Conference\n\n\nAbstract\nThis talk will describe connections betw
een structural results about the finite simple groups and the complexity o
f computational algorithms for permutation groups.\n\nThe first part of th
e talk will discuss the base size of a permutation group\, an invariant wh
ich determines the complexity of many permutation group algorithms. We wil
l present a new\, optimal\, bound on the base size of the primitive groups
that are not large base. After this\, we will discuss some group-theoreti
c questions for which there is no known polynomial time solution. In parti
cular\, we shall present a new approach to computing the normaliser of a p
rimitive group $G$ in an arbitrary subgroup $H$ of $S_{n}$. Our method run
s in quasipolynomial time $O(2^{log^3 n})$\, whereas the previous best kno
wn algorithm required time $O(2^n)$.\n\nThis is partly joint work with Mar
iapia Moscatiello (Padova)\, and partly with Sergio Siccha (Siegen).\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andrei Jaikin-Zapirain (Autonomous University of Madrid)
DTSTART:20201015T150000Z
DTEND:20201015T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/2
DESCRIPTION:Title: Intersection of subgroups in a surface group\nby Andrei Jaikin-Z
apirain (Autonomous University of Madrid) as part of GOThIC - Ischia Onlin
e Group Theory Conference\n\n\nAbstract\nLet $G$ be a surface group\, i.e
the fundamental group of a compact surface. Denote by $d(G)$ the number of
generators of $G$ and by $\\chi(G)$ the Euler characteristic of $G$. We p
ut $\\bar \\chi(G) = \\max\\{0\, −\\chi(G)\\}$.\n\nIn this talk I will e
xplain the following two results. In the first result we prove that for an
y two finitely generated subgroups $U$ and $W$ of $G$\,\n\n$$\n\\sum_{x \\
in U\\backslash G / W} \\bar \\chi (U \\cap x W x^{-1}) \\le \\bar \\chi(U
) \\cdot \\bar\\chi(W).\n$$\nFrom this we obtain the Strengthened Hanna Ne
umann conjecture for non-solvable surface groups. In the second result we
show that if $R$ is a retract of $G$\, then for any finitely generated sub
group $H$ of $G$\,\n$$\nd(R \\cap H) \\le d(H).\n$$\nThis implies the Dick
s-Ventura inertia conjecture for free groups. The talk is based on a joint
work with Yago Antolín.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Anitha Thillaisundaram (University of Lincoln)
DTSTART:20201022T150000Z
DTEND:20201022T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/3
DESCRIPTION:Title: The congruence subgroup property for multi-EGS groups\nby Anitha
Thillaisundaram (University of Lincoln) as part of GOThIC - Ischia Online
Group Theory Conference\n\n\nAbstract\nIt was proved by G. A. Fernández-
Alcober\, A. Garrido and J. Uria-Albizuri that the branch Grigorchuk-Gupta
-Sidki (GGS) groups possess the congruence subgroup property. This result
was extended to all branch multi-GGS groups by A. Garrido and J. Uria-Albi
zuri. The extended Gupta-Sidki (EGS) groups\, which were the first example
s of finitely generated branch groups without the congruence subgroup prop
erty\, were constructed by Pervova. In this talk\, we consider a natural g
eneralisation of multi-GGS and EGS groups\, and demonstrate their unexpect
ed behaviour concerning the congruence subgroup property. This is joint wo
rk with J. Uria-Albizuri.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Bettina Eick (Technical University of Braunschweig)
DTSTART:20201029T160000Z
DTEND:20201029T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/4
DESCRIPTION:Title: Groups and their integral group rings\nby Bettina Eick (Technica
l University of Braunschweig) as part of GOThIC - Ischia Online Group Theo
ry Conference\n\n\nAbstract\nThe integral group ring $\\mathbb{Z} G$ of a
group $G$ plays an important role in the theory of integral representation
s. This talk gives a brief introduction to this topic and then shows how s
uch group rings can be investigated using computational tools. In particul
ar\, the quotients $I^n(G)/I^{n+1}(G)$\, where $I^n(G)$ is the $n$-th powe
r ideal of the augmentation ideal $I(G)$\, are an interesting invariant of
the group ring $\\mathbb{Z} G$ and we show how to determine them for give
n $n$ and given finitely presented $G$. We then exhibit a variety of examp
le applications for finite and infinite groups $G$.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Derek J. S. Robinson (University of Illinois at Urbana-Champaign)
DTSTART:20201105T160000Z
DTEND:20201105T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/5
DESCRIPTION:Title: The seriality problem for Sylow-permutable subgroups in locally fini
te groups\nby Derek J. S. Robinson (University of Illinois at Urbana-C
hampaign) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nA
bstract\nA subgroup $H$ of a group $G$ is said to be weakly Sylow permutab
le in $G$ if $HP=PH$ for all Sylow subgroups $P$ of $G$ and all primes $p$
dividing orders of elements of $H$. Otto Kegel proved that if $G$ is fini
te\, then $H$ is subnormal in $G$. This does not hold for infinite groups.
The Seriality Problem is whether Kegel’s theorem can be extended to loc
ally finite groups if "subnormal” is replaced by “serial”. I will di
scuss the background to the problem and recent progress towards its soluti
on.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alexander Bors ((Johann Radon Institute for Compu- tational and Ap
plied Mathematics)
DTSTART:20201112T160000Z
DTEND:20201112T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/6
DESCRIPTION:Title: Groups with few automorphism orbits\nby Alexander Bors ((Johann
Radon Institute for Compu- tational and Applied Mathematics) as part of GO
ThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nLet $G$ be a g
roup\, and consider the natural action of the automorphism group of $G$ on
$G$. The orbits of this action are called the automorphism orbits of $G$.
In this talk\, we will give an overview of known results concerning group
s with finitely many automorphism orbits\, including results where $G$ is
assumed to have a concrete\, small number of automorphism orbits\, such as
$G$. We will then speak in more detail about a result\, achieved in colla
boration with Stephen Glasby from UWA (Perth)\, which provides a full clas
sification of the finite $2$-groups with exactly three automorphism orbits
.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ramón Esteban-Romero (Polytechnic University of Valencia)
DTSTART:20201119T160000Z
DTEND:20201119T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/7
DESCRIPTION:Title: Triply factorised groups and skew left braces\nby Ramón Esteban
-Romero (Polytechnic University of Valencia) as part of GOThIC - Ischia On
line Group Theory Conference\n\n\nAbstract\nThe Yang-Baxter equation is a
consistency equation of the statistical mechanics\nproposed by Yang [Yang6
7] and Baxter\n[Baxter73] that describes the interaction of many particles
in some scattering\nsituations. This equation lays the foundation for the
theory of quantum\ngroups and Hopf algebras. During the last years\, the
study suggested by\nDrinfeld [Drinfeld92] of the so-called\nset-theoretic
solutions of the Yang-Baxter equation has motivated the\nappearance of man
y algebraic structures. Among these structures we\nfind the *skew left bra
ces*\, introduced by Guarnieri and\nVendramin [GuarnieriVendramin17] as a
generalisation of the\nstructure of left brace defined by Rump [Rump07].
It consists of a set $B$\nwith two operations $+$ and $\\cdot$\, not neces
sarily commutative\, that give $B$ two structures of\ngroup linked by a mo
dified distributive law.\n\nThe multiplicative group $C=(B\, {\\cdot})$ of
a skew left brace $(B\, {+}\, {\\cdot})$\nacts on the\nmultiplicative gro
up $K=(B\, {+})$ by means of an action $\\lambda\\colon\nC\\longrightarrow
\\operatorname{Aut}(K)$ given by\n$\\lambda(a)(b)=-a+a\\cdot b$\, for $a$
\, $b\\in B$. With respect to this\naction\, the identity map $\\delta\\co
lon C\\longrightarrow K$ becomes a\nderivation or $1$-cocycle with respect
to $\\lambda$. In the semidirect\nproduct $G=[K]C=\\{(k\,c)\\mid k\\in K\
, c\\in C\\}$\, there is a\ndiagonal-type subgroup $D=\\{(\\delta(c)\, c)\
\mid c\\in C\\}$ such that\n$G=KD=CD$\, $K\\cap D=C\\cap D=1$. This approa
ch was presented by\nSysak in [Sysak11-PortoCesareo] and motivates the use
of\ntechniques of group theory to study skew left braces.\n\nWe present i
n this talk some applications of this approach to obtain\nsome results abo
ut skew left braces. These results have been obtained\nin collaboration wi
th Adolfo Ballester-Bolinches.\n\nThis work has been supported by the rese
arch grants\nPGC2018-095140-B-I00 from the Ministerio de Ciencia\,\n Inno
vaci\\'on y Universidades (Spanish Government)\, the\nAgencia Estatal de I
nvestigaci\\'on (Spain)\, and FEDER (European\nUnion)\, and PROMETEO/2017/
057 from the Generalitat\n(Valencian Community\, Spain).\n\nReferences\n\n
[Baxter73] R. Baxter. Eight-vertex model in lattice statistics and one-dim
ensional\nanisotropic Heisenberg chain. I. Some fundamental eigenvectors.
Ann.\nPhysics\, 76(1):1–24\, 1973.\n\n[Drinfeld92] V. G. Drinfeld. On so
me unsolved problems in quantum group theory.\nIn P. P. Kulish\, editor\,
Quantum groups. Proceedings of workshops held\nin the Euler International
Mathematical Institute\, Leningrad\, fall 1990\,\nvolume 1510 of Lecture N
otes in Mathematics\, pages 1–8. Springer-Verlag\,\nBerlin\, 1992.\n\n[G
uarnieriVendramin17] L. Guarnieri and L. Vendramin. Skew-braces and the Ya
ng-Baxter equation. Math. Comp.\, 86(307):2519–2534\, 2017.\n\n[Rump07]
W. Rump. Braces\, radical rings\, and the quantum Yang-Baxter equation.\nJ
. Algebra\, 307:153–170\, 2007.\n\n[Sysak11-PortoCesareo] Y. P. Sysak. P
roducts of groups and quantum Yang-Baxter equation.\nNotes of a talk in Ad
vances in Group Theory and Applications\, Porto\nCesareo\, Lecce\, Italy\,
2011.\n\n[Yang67] C. N. Yang. Some exact results for many-body problem in
one dimension\nwith repulsive delta-function interaction. Phys. Rev. Lett
\, 19:1312–1315\,\n1967\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Urban Jezernik (Alfréd Rényi Institute of Mathematics)
DTSTART:20201126T160000Z
DTEND:20201126T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/8
DESCRIPTION:Title: Diameters of groups\nby Urban Jezernik (Alfréd Rényi Institute
of Mathematics) as part of GOThIC - Ischia Online Group Theory Conference
\n\n\nAbstract\nThe diameter of a finite group $G$ equipped with a generat
ing set $S$ is the smallest number $k$ so that every element of $G$ can be
written as a product of at most $k$ elements from $S$. We will take a loo
k at how large or small these diameters can (conjecturally) be\, and what
the generic situation is like.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gareth Tracey (University of Oxford)
DTSTART:20201203T160000Z
DTEND:20201203T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/9
DESCRIPTION:Title: On the Fitting height and insoluble length of a finite group\nby
Gareth Tracey (University of Oxford) as part of GOThIC - Ischia Online Gr
oup Theory Conference\n\n\nAbstract\nA classical result of Baer states tha
t an element x of a finite group $G$ is contained in the Fitting subgroup
$F(G)$ of $G$ if and only if $x$ is a left Engel element of $G$. That is\,
$x$ is in $F(G)$ if and only if there exists a positive integer $k$ such
that $[g\, x\, ...\, x]$ (with $x$ appearing $k$ times\, and using the con
vention $[x_1\, x_2\, x_3\, \\dots\, x_k] := [[\\dots [[x_1\, x_2]\, x_3]\
, ...]\, x_k])$ is trivial for all $g$ in $G$. The result was generalised
by E. Khukhro and P. Shumyatsky in a 2013 paper via an analysis of the set
s $E(G(k))= \\{[g\, x\, ...\, x]: g \\in G\\}$.\n\nIn this talk\, we will
continue to study the properties of these sets\, concluding with the proof
of two conjectures made in said paper. As a by-product of our methods\, w
e also prove a generalisation of a result of Flavell\, which itself genera
lises Wielandt's Zipper Lemma and provides a characterisation of subgroups
contained in a unique maximal subgroup. We also derive a number of conseq
uences of our theorems\, including some applications to the set of odd ord
er elements of a nite group inverted by an involutory automorphism. Joint
work with R.M. Guralnick.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Donald S. Passman (University of Wisconsin-Madison)
DTSTART:20201210T160000Z
DTEND:20201210T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/10
DESCRIPTION:Title: Polynomial Identities\, Permutational Groups and Rewritable Groups<
/a>\nby Donald S. Passman (University of Wisconsin-Madison) as part of GOT
hIC - Ischia Online Group Theory Conference\n\n\nAbstract\nWe first study
groups whose group algebras satisfy a polynomial identity. We then conside
r permutational groups and rewritable groups. We discuss the known charact
erizations of such groups and the relationships between these three group-
theoretic properties and also between the proofs of their corresponding ma
in theorems. Finally we discuss certain parameters associated with these c
onditions and we mention a number of examples of interest.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Francesco Matucci (Università di Milano-Bicocca)
DTSTART:20201217T160000Z
DTEND:20201217T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/11
DESCRIPTION:Title: On Finitely Presented Groups that Contain $\\mathbb{Q}$\nby Fra
ncesco Matucci (Università di Milano-Bicocca) as part of GOThIC - Ischia
Online Group Theory Conference\n\n\nAbstract\nIt is a consequence of Higma
n's embedding theorem that the additive group $\\mathbb{Q}$ of rational nu
mbers can be embedded into a finitely presented group. Though Higman's pro
of is constructive\, the resulting group presentation would be very large
and unpleasant. In 1999\, Martin Bridson and Pierre de la Harpe asked for
an explicit and "natural" example of a finitely presented group that conta
ins an embedded copy of $\\mathbb{Q}$. In this talk\, we describe some sol
utions to the Bridson - de la Harpe problem related to Richard Thompson's
groups F\, T\, and V. Moreover\, we prove that there exists a group contai
ning $\\mathbb{Q}$ which is simple and has type F infinity. This is joint
work with Jim Belk and James Hyde.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alex Lubotzky (Hebrew University of Jerusalem)
DTSTART:20210114T150000Z
DTEND:20210114T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/12
DESCRIPTION:Title: Stability\, non-approximated groups and high-dimensional expanders<
/a>\nby Alex Lubotzky (Hebrew University of Jerusalem) as part of GOThIC -
Ischia Online Group Theory Conference\n\n\nAbstract\nSeveral well-known o
pen questions\, such as: "are all groups sofic or hyperlinear?"\, have a c
ommon form: can all groups be approximated \nby asymptotic homomorphisms i
nto the symmetric groups $\\mathrm{Sym}(n)$ (in the sofic case) or the un
itary groups $U(n)$ (in the hyperlinear case)?\n\n In the case of $U(
n)$\, the question can be asked with respect to different metrics and norm
s. \n We answer\, for the first time\, some of these versions\, showi
ng that there exist finitely presented groups which are not approximated
by $U(n)$ with respect to the Frobenius ($=L_2$) norm and many other norms
.\n\n The strategy is via the notion of "stability": Some higher dimens
ional cohomology vanishing phenomena is proven to imply stability. Using G
arland method ( a.k.a. high dimensional expanders as quotients of Bruhat-
Tits buildings)\, it is shown that some non-residually-finite groups ar
e stable and hence cannot be approximated. These groups are central exten
sions of some lattices in p-adic Lie groups (constructed via a p-adic ver
sion of a result of Deligne).\n\n All notions will be explained.
Based on joint works with M. De Chiffre\, L. Glebsky and A. Thom and wit
h I. Oppenheim .\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eugenio Giannelli (Università di Firenze)
DTSTART:20210204T160000Z
DTEND:20210204T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/13
DESCRIPTION:Title: Sylow Branching Coefficients and a Conjecture of Malle and Navarro<
/a>\nby Eugenio Giannelli (Università di Firenze) as part of GOThIC - Isc
hia Online Group Theory Conference\n\n\nAbstract\nLet $G$ be a finite grou
p and let $P$ be a Sylow subgroup of $G$.\n\nIn 2012 Malle and Navarro con
jectured that $P$ is normal in $G$ if and only if the permutation characte
r associated to the natural action of $G$ on the cosets of $P$ has some sp
ecific structural properties. In recent joint work with Law\, Long and Val
lejo we prove this conjecture. \n\nWe will start this talk by describing t
he problem and its relevance in the context of representation theory of fi
nite groups. \n\nThen we will introduce and review some recent results on
Sylow Branching Coefficients for symmetric groups.\n\nFinally we will talk
about the crucial role played by these objects in our proof of the conjec
ture.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Mima Stanojkovski (Max-Planck-Institut Leipzig)
DTSTART:20210121T160000Z
DTEND:20210121T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/14
DESCRIPTION:Title: On the modular isomorphism problem for groups of class $3$\nby
Mima Stanojkovski (Max-Planck-Institut Leipzig) as part of GOThIC - Ischia
Online Group Theory Conference\n\n\nAbstract\nLet $G$ be a finite group a
nd let $R$ be a commutative ring. In 1940\, G.\nHigman asked whether the i
somorphism type of $G$ is determined by its\ngroup ring $RG$. Although the
Isomorphism Problem has generally a negative\nanswer\, the Modular Isomor
phism Problem (MIP)\, for $G$ a $p$-group and $R$ a\nfield of positive cha
racteristic $p$\, is still open. Examples of $p$-groups\nfor which the (MI
P) has a positive solution are abelian groups\, groups\nof order dividing
$2^9$ or $3^7$ or $p^5$\, certain groups of maximal class\,\netc.\n\nI wil
l give an overview of the history of the (MIP) and will present\nrecent jo
int work with Leo Margolis for groups of nilpotency class $3$. In\nparticu
lar\, our results yield new families of groups of order $p^6$ and\n$p^7$ f
or which the (MIP) has a positive solution and a new invariant for certain
\n$2$-generated groups of class $3$.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Iker de las Heras Kerejeta (University of the Basque Country)
DTSTART:20210128T160000Z
DTEND:20210128T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/15
DESCRIPTION:Title: Hausdorff dimension and Hausdorff spectra in profinite groups\n
by Iker de las Heras Kerejeta (University of the Basque Country) as part o
f GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nThe Hausdo
rff dimension is a generalisation of the usual concept of dimension which
allows to define the dimension of fractal sets in metric spaces. In the la
st decades\, this notion has led to fruitful applications in the context o
f countably based profinite groups\, as these groups can be naturally seen
as metric spaces with respect to a given filtration series.\n\nIn this ta
lk we will give a brief introduction to this topic and we will overview so
me of the main related properties. Finally\, we will present some results
concerning the so-called (normal) Hausdorff spectra of a given profinite g
roup\, which reflect the range of Hausdorff dimensions of closed (normal)
subgroups.\n\nJoint work with Benjamin Klopsch and Anitha Thillaisundaram.
\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Kıvanç Ersoy (Freie Universität Berlin)
DTSTART:20210211T160000Z
DTEND:20210211T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/16
DESCRIPTION:Title: On the centralizer depth in simple locally finite groups\nby K
ıvanç Ersoy (Freie Universität Berlin) as part of GOThIC - Ischia Onlin
e Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Norberto Gavioli (Università degli Studi dell'Aquila)
DTSTART:20210218T160000Z
DTEND:20210218T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/17
DESCRIPTION:Title: Thin subalgebras of Lie algebras of maximal class\nby Norberto
Gavioli (Università degli Studi dell'Aquila) as part of GOThIC - Ischia O
nline Group Theory Conference\n\n\nAbstract\nJoint work with M. Avitabile\
, A. Caranti\, V. Monti\, M. F. Newman and E. O'Brien\n\nLet $L$ be an inf
inite dimensional Lie algebra which is graded over the positive integers a
nd is generated by its first homogeneous component $L_1$. The algebra $L$
is of maximal class if $\\dim(L_1)=2$ and $\\dim(L_i)=1$ for $1$ larger th
an $1$. The algebra $L$ is thin if it is not of maximal class\, $\\dim(L_1
)=2$ and $L_{i+1}=[x\,L_1]$ for any nontrivial element $x$ in $L_i$.\n\nSu
ppose that $E$ is a quadratic extension of a field $F$ and that $M$ is a L
ie algebra of maximal class over $E$. We consider the Lie algebra $L$ gene
rated over the field $F$ by an $F$-subspace $L_1$ of $M_1$ having dimensio
n $2$ over $F$. We give necessary and sufficient conditions for the lie al
gebra $L$ to be a thin graded $F$-subalgebra of the $F$-algebra $M$. We sh
ow also that there are uncountably many such thin algebras that can be con
structed by way of this “recipe”\, attaining the maximum possible card
inality.\n\nThe authors started this project almost independently since 19
99 and their partial results have been luckily and duly recorded by A. Car
anti. Only recently we have been able to develop together thorough and con
cise results for this research.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Agnieszka Bier (Silesian University of Technology)
DTSTART:20210225T160000Z
DTEND:20210225T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/18
DESCRIPTION:Title: On weak Sierpinski subsets in groups\nby Agnieszka Bier (Silesi
an University of Technology) as part of GOThIC - Ischia Online Group Theor
y Conference\n\n\nAbstract\nA subset $E$ in a group $G$ is called a weak S
ierpinski subset if for some $g\, h$ in $G$ and $a$ different from $b$ in
$E$\, we have $gE = E \\setminus \\{a\\}$ and $hE = E \\setminus \\{b\\}$.
In the talk we discuss the subgroup generated by $g$ and $h$\, and show t
hat either it is free over $(g\,h)$ or it has presentation $G(k)=\\left\\
langle g\, h \\mid (h^{-1}g)^k \\right\\rangle$. We also characterize all
weak Sierpinski subsets in the groups $G(k)$. This is joint work with Y. C
ornulier and P. Slanina.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cristina Acciarri (Universidade de Brasília)
DTSTART:20210304T160000Z
DTEND:20210304T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/19
DESCRIPTION:Title: A stronger version of Neumann’s BFC-theorem\nby Cristina Acci
arri (Universidade de Brasília) as part of GOThIC - Ischia Online Group T
heory Conference\n\n\nAbstract\nA celebrated theorem of B. H. Neumann stat
es that if $G$ is a group in which all conjugacy classes are finite with b
ounded size\, then the derived group $G’$ is finite. \n\nIn this talk we
will discuss a stronger version of Neumann’s result and some corollarie
s for finite and profinite groups. Based on a joint work with Pavel Shumya
tsky.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/19/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gunter Malle (Technische Universität Kaiserslautern)
DTSTART:20210311T160000Z
DTEND:20210311T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/20
DESCRIPTION:Title: Conjugacy class numbers and $\\pi$-subgroups\nby Gunter Malle (
Technische Universität Kaiserslautern) as part of GOThIC - Ischia Online
Group Theory Conference\n\n\nAbstract\nWe will discuss relations between t
he number of conjugacy classes of a finite group and that of proper subgro
ups. On the way\, we'll encounter the so-called almost abelian groups (a t
erm coined by J. Thompson). We then connect this to obtaining estimates f
or the number of Brauer characters in a Brauer block of a finite group. Th
is is joint work with Gabriel Navarro and Geoffrey Robinson.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Britta Spaeth (Bergische Universität Wuppertal)
DTSTART:20210318T160000Z
DTEND:20210318T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/21
DESCRIPTION:Title: Representation Theory above Spin Groups - Another Step towards the
McKay Conjecture\nby Britta Spaeth (Bergische Universität Wuppertal)
as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nI
n the representation theory of finite groups it is suspected that the repr
esentation theory of a group is already determined by its local subgroups.
This lead to numerous conjectures like the McKay conjecture. During the l
ast decade substantial progress in a final proof of the McKay conjecture h
as been made. After an overview of the development I sketch the open quest
ions\, that are mainly regarding the representation theory of spin groups
and some progress made on one of those questions.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/21/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas M. Keller (Texas State University)
DTSTART:20210422T150000Z
DTEND:20210422T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/22
DESCRIPTION:Title: Character degrees\, conjugacy class sizes\, and element orders: thr
ee primes\nby Thomas M. Keller (Texas State University) as part of GOT
hIC - Ischia Online Group Theory Conference\n\n\nAbstract\nThere are many
results that give information on the structure\nof a finite group in terms
of properties that refer to its character degrees/\nclass sizes/element o
rders and at most two primes. In this talk we present\na first attempt to
extend some of these results considering three primes. We concentrate on b
ounds for the Fitting height of solvable groups. (This is joint \nwork wit
h Alex Moreto.)\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/22/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Various (Various)
DTSTART:20210325T160000Z
DTEND:20210325T225900Z
DTSTAMP:20260404T111246Z
UID:GOThIC/23
DESCRIPTION:Title: 24 Hours of Ischia Group Theory\nby Various (Various) as part o
f GOThIC - Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/23/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Various (Various)
DTSTART:20210325T230000Z
DTEND:20210326T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/24
DESCRIPTION:Title: 24 Hours of Ischia Group Theory\nby Various (Various) as part o
f GOThIC - Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/24/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eamonn O'Brien (The University of Auckland)
DTSTART:20210415T090000Z
DTEND:20210415T100000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/25
DESCRIPTION:Title: Constructing composition factors for linear groups\nby Eamonn O
'Brien (The University of Auckland) as part of GOThIC - Ischia Online Grou
p Theory Conference\n\n\nAbstract\nA recent result of Holt\, Leedham-Green
and O'Brien shows that we are\nfinally in a position where\, subject to c
ertain assumptions\, we\ncan construct in polynomial time the composition
factors of a\nsubgroup of $\\mathrm{GL}(d\, q)$. The principal components
are "constructive recognition" and presentations on "standard generators"
for the finite simple groups. We survey this work.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/25/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Evgeny Plotkin (Bar-Ilan University)
DTSTART:20210429T150000Z
DTEND:20210429T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/26
DESCRIPTION:Title: Rigid logical characterizations of linear and Kac-Moody groups\
nby Evgeny Plotkin (Bar-Ilan University) as part of GOThIC - Ischia Online
Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/26/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Natalia Maslova (Russian Academy of Sciences)
DTSTART:20210506T150000Z
DTEND:20210506T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/27
DESCRIPTION:Title: On pronormality of subgroups of odd index in finite groups\nby
Natalia Maslova (Russian Academy of Sciences) as part of GOThIC - Ischia O
nline Group Theory Conference\n\n\nAbstract\nIn this talk we discuss a rec
ent progress in research of pronormality of subgroups of odd index in fini
te groups.\n\nA subgroup $H$ of a group $G$ is pronormal in $G$ if for any
element $g$ from $G$\, subgroups $H$ and $H^g$ are conjugate in the subgr
oup $\\langle H\, H^g \\rangle$ generated by $H$ and $H^g$. Some problems
in Finite Group Theory\, Combinatorics\, and Permutation Group Theory were
solved in terms of pronormality (see\, for example\, remarkable results b
y L. Babai\, P. Palfy\, Ch. Praeger\, and others). Thus\, the question of
description of families of pronormal subgroups in finite groups is of inte
rest. Well-known examples of pronormal subgroups in finite groups are norm
al subgroups\, maximal subgroups\, Sylow subgroups\, Carter subgroups\, Ha
ll subgroups of solvable groups\, and so on.\n\nIn 2012\, E.P. Vdovin and
D.O. Revin proved that the Hall subgroups are pronormal in finite simple g
roups and conjectured that the subgroups of odd index are pronormal in fin
ite simple groups. This conjecture was disproved by A.S. Kondrat'ev\, the
speaker\, and D. Revin in 2016. However\, in many finite simple groups the
subgroups of odd index are pronormal. Moreover\, the question of pronorma
lity of a subgroup of odd index in an arbitrary finite group can be partia
lly reduced to questions of pronormality of some subgroups of odd indices
in its chief factors.\n\nThis talk is partially based on joint results wit
h S. Glasby\, A.S. Kondrat’ev\, C.E. Praeger\, and D.O. Revin.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/27/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laurent Bartholdi (Georg-August Universität zu Göttingen)
DTSTART:20210513T150000Z
DTEND:20210513T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/28
DESCRIPTION:Title: Dimension series and homotopy groups of spheres\nby Laurent Bar
tholdi (Georg-August Universität zu Göttingen) as part of GOThIC - Ischi
a Online Group Theory Conference\n\n\nAbstract\nThe lower central series o
f a group $G$ is defined by $\\gamma_1=G$ and $\\gamma_n = [G\,\\gamma_{n-
1}]$. The "dimension series"\, introduced by Magnus\, is defined using the
group algebra over the integers: $$\\delta_n = \\{g: g-1\\text{ belongs t
o the $n$-th power of the augmentation ideal}\\}.$$\n\nIt has been\, for t
he last 80 years\, a fundamental problem of group theory to relate these t
wo series. One always has $\\delta_n\\ge\\gamma_n$\, and a conjecture by M
agnus\, with false proofs by Cohn\, Losey\, etc.\, claims that they coinci
de\; but Rips constructed an example with $\\delta_4/\\gamma_4$ cyclic of
order 2. On the positive side\, Sjogren showed that $\\delta_n/\\gamma_n$
is always a torsion group\, of exponent bounded by a function of $n$. Furt
hermore\, it was believed (and falsely proven by Gupta) that only $2$-tors
ion may occur.\n\nIn joint work with Roman Mikhailov\, we prove however th
at every torsion abelian group may occur as a quotient $\\delta_n/\\gamma_
n$\; this proves that Sjogren's result is essentially optimal.\n\nEven mor
e interestingly\, we show that this problem is intimately connected to the
homotopy groups $\\pi_n^(S^m)$ of spheres\; more precisely\, the quotient
$\\delta_n/\\gamma_n$ is related to the difference between homotopy and h
omology. We may explicitly produce $p$-torsion elements starting from the
order-$p$ element in the homotopy group $\\pi_{2p}(S^2)$ due to Serre.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/28/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Péter Pál Pálfy (Hungarian Academy of Sciences)
DTSTART:20210527T150000Z
DTEND:20210527T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/29
DESCRIPTION:Title: Galois and PSL\nby Péter Pál Pálfy (Hungarian Academy of Sci
ences) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbst
ract\nIn his "testamentary letter" Galois claims\n(without proof) that $\\
text{PSL}(2\,p)$ does not have a subgroup of index $p$\nwhenever $p>11$\,
and gives examples that for $p = 5\, 7\, 11$ such subgroups\nexist. \n\nTh
e attempt by Betti in 1853 to give a proof does not seem to be\ncomplete.
Jordan's proof in his 1870 book uses methods certainly not\nknown to Galoi
s. Nowadays we deduce Galois's result from the complete\nlist of subgroups
of $\\text{PSL}(2\,p)$ obtained by Gierster in 1881.\n\nIn the talk I wil
l give a proof that might be close to Galois's own\nthoughts. \n\nLast Oct
ober I exchanged a few e-mails on this topic with\nPeter M. Neumann. So th
e talk is in some way a commemoration of him.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/29/
END:VEVENT
BEGIN:VEVENT
SUMMARY:John S. Wilson (Cambridge and Leipzig)
DTSTART:20210603T150000Z
DTEND:20210603T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/30
DESCRIPTION:Title: A first-order perspective on finite groups\nby John S. Wilson (
Cambridge and Leipzig) as part of GOThIC - Ischia Online Group Theory Conf
erence\n\n\nAbstract\nThe finite axiomatizability of classes of finite gro
ups\, and the definability of naturally occurring subgroups\, have attract
ed considerable attention. In this talk\, some of the results\, positive
and definite\, will be discussed\, and it will be shown that the strikingl
y different behaviour of certain properties seems to be reflected in (non-
first-order) studies of these properties.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/30/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Skipper (Ohio State University)
DTSTART:20210610T150000Z
DTEND:20210610T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/31
DESCRIPTION:Title: The Cantor-Bendixson rank of the Grigorchuk group\nby Rachel Sk
ipper (Ohio State University) as part of GOThIC - Ischia Online Group Theo
ry Conference\n\n\nAbstract\nThe space of subgroups of a group has a natur
al Polish topology and understanding this space can help to understand the
group. In this talk\, we will consider the Cantor-Bendixson derivative an
d rank for the space of subgroups of the Grigorchuk group\, using it to st
ratify the subgroups of this group. This is a joint work with Phillip Weso
lek.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/31/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Thomas Weigel (Università di Milano Bicocca)
DTSTART:20210520T150000Z
DTEND:20210520T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/32
DESCRIPTION:Title: Maximal pro $p$-quotients of absolute Galois groups\nby Thomas
Weigel (Università di Milano Bicocca) as part of GOThIC - Ischia Online G
roup Theory Conference\n\n\nAbstract\n(Joint work with Claudio Quadrelli.)
\n\nIt is well-known that the absolute Galois group $G_K = \\operatorname{
Gal}(\\bar K^{\\text{sep}}/K)$ of a field $K$\nis a profinite group. Howev
er\, only in very restrictive circumstances it is possible to\nanalyze the
structure of $G_K$ completely. A first approximation - which is untertake
n\nfrequently - is to investigate the maximal pro-$p$ quotient $G_K(p) = G
_K/O^{p}\n(G_K)$ for a prime $p$. Here $O_p(\\_)$ is the closed subgroup b
eing generated by all Sylow\npro-$\\ell$ subgroups for $\\ell \\ne p$. The
absolute Galois group $G_K$ comes equipped with a\ncontinuous group homom
orphism\n$$\n\\theta_{K\,p} : G_K \\to \\mathbb{Z}_p^{x}\n\,$$\nthe $p$-cy
clotomic character\, where $\\mathbb{Z}_p^{x}$ denotes group of the invert
ible elements in\nthe ring of $p$-adic integers $\\mathbb{Z}_p$. In case t
hat $K$ contains a primitive $p$-th root of unity\,\nthe homomorphism $\\t
heta_{K\,p}$ is induced from a group homomorphism\n$$\n\\hat\\theta_{K\,p}
: G_K(p) \\to \\mathbb{Z}_p^{x}\n.$$\n\nA pro-$p$ group $G$ together with
a continuous group homomorphism $\\theta : G → \\mathbb{Z}_p^{x}$\nis\n
also called an oriented pro-$p$ group. Although the structure of $G_K(p)$
is in general\nmuch easier to analyze than $G_K$ there are still many open
questions concerning\nthe oriented pro-$p$ groups $(G_K(p)\, \\hat\\theta
_{K\,p})$. E.g.\, around 25 years ago it was conjectured by I. Efrat\, tha
t in case that $G_K(p)$ is a finitely generated pro-$p$ group\,\nthen $(G_
K(p)\, \\hat\\theta_{K\,p})$ must be of elementary type. Here one defines
the class of oriented pro-$p$ groups of elementary type as the smallest cl
ass of oriented pro-$p$ groups\nwhich is closed under free products\, and
fibre products with $\\theta$-abelian oriented pro-$p$ groups which contai
ns $(F\, \\alpha)$ for all finitely generated free pro-$p$ groups $F$ and
any $\\alpha : F \\to \\mathbb{Z}_p^{x}$\, as well as $(D\, \\eth)$ for al
l Demush’kin pro-$p$ groups $D$\, where $\\eth: D \\to \\mathbb{Z}_p^{x}
$ is the $p$-orientation induced by the dualizing module of D. In the talk
I will discuss recent developments in Field theory\, which transformed I.
Efrat’s elementary\ntype conjecture into a purely group theoretic quest
ion. Recently\, this question\nhas been investigated successfully for cert
ain classes of oriented pro-$p$ groups: 1)\nRight-angled Artin pro-$p$ gro
ups with trivial orientation (I. Snopce\, P. Zalesskii)\,\n2) Generalized
right-angled Artin pro-$p$ groups (S. Blumer\, C. Quadrelli\, T.W.).\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/32/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Rachel Camina (University of Cambridge)
DTSTART:20210701T150000Z
DTEND:20210701T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/33
DESCRIPTION:Title: Word problems for finite nilpotent groups\nby Rachel Camina (Un
iversity of Cambridge) as part of GOThIC - Ischia Online Group Theory Conf
erence\n\n\nAbstract\nWe consider word maps on finite nilpotent groups and
count the sizes of the fibres for elements in the image. We consider Amit
’s conjecture and its generalisation\, which say that these fibres shoul
d have size at least $\\lvert G \\rvert^{k−1}$\, where the word is on $k
$ variables. This is joint work with Ainhoa Iñiguez and Anitha Thillaisun
daram.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/33/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Giles Gardam (University of Münster)
DTSTART:20210708T150000Z
DTEND:20210708T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/34
DESCRIPTION:Title: Kaplansky's conjectures\nby Giles Gardam (University of Münste
r) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract
\nThree conjectures on group rings of torsion-free groups are commonly att
ributed to Kaplansky\, namely the unit\, zero divisor and idempotent conje
ctures. For example\, the zero divisor conjecture predicts that if $K$ is
a field and $G$ is a torsion-free group\, then the group ring $K[G]$ has n
o zero divisors. I will survey what is known about the conjectures\, inclu
ding their relationships to each other and to other conjectures and group
properties\, and present my recent counterexample to the unit conjecture.\
n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/34/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dan Segal (University of Oxford)
DTSTART:20210617T150000Z
DTEND:20210617T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/35
DESCRIPTION:Title: Groups\, Rings\, Logic\nby Dan Segal (University of Oxford) as
part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\nIn g
roup theory\, interesting statements about a group usually can’t be ex-\
npressed in the language of first-order logic. It turns out\, however\, th
at some\ngroups can actually be determined by their first-order properties
\, or\, even more\nstrongly\, by a single first-order sentence. In the lat
ter case the group is said to\nbe finitely axiomatizable.\n\nI will descri
be some examples of this phenomenon (joint work with A. Nies\nand K. Tent)
. One family of results concerns axiomatizability of $p$-adic analytic\npr
o-$p$ groups\, within the class of all profinite groups.\n\nAnother main r
esult is that for an adjoint simple Chevalley group of rank at\nleast $2$
and an integral domain $R$\, the group $G(R)$ is bi-interpretable with the
\nring $R$. This means in particular that first-order properties of the gr
oup $G(R)$\ncorrespond to first-order properties of the ring $R$. As many
rings are known to\nbe finitely axiomatizable we obtain the corresponding
result for many groups\;\nthis holds in particular for every finitely gene
rated group of the form $G(R)$.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/35/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Nikolay Nikolov (University of Oxford)
DTSTART:20210624T150000Z
DTEND:20210624T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/36
DESCRIPTION:Title: On profinite groups with positive rank gradient\nby Nikolay Nik
olov (University of Oxford) as part of GOThIC - Ischia Online Group Theory
Conference\n\n\nAbstract\nIn this talk I will introduce rank gradient of
groups and discuss open questions about groups with positive rank gradient
. In the second part I will focus on the profinite situation and sketch a
proof that a profinite group $G$ with positive rank gradient does not sati
sfy a group law.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/36/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Cindy (Sin Yi) Tsang (Ochanomizu University)
DTSTART:20210715T130000Z
DTEND:20210715T140000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/37
DESCRIPTION:Title: The multiple holomorph of centerless groups\nby Cindy (Sin Yi)
Tsang (Ochanomizu University) as part of GOThIC - Ischia Online Group Theo
ry Conference\n\n\nAbstract\nThe holomorph $\\operatorname{Hol}(G)$ of a g
roup $G$ may be defined as the normalizer of the subgroup of left translat
ions in the group of all permutations of $G$. The multiple holomorph $\\op
eratorname{NHol}(G)$ of $G$ may in turn be defined as the normalizer of th
e holomorph. Their quotient $T(G) = \\operatorname{NHol}(G)/\\operatorname
{Hol}(G)$ has been computed for various families of groups G\, and interes
tingly $T(G)$ turns out to be elementary $2$-abelian in many of the known
cases. In this talk\, we consider the case when $G$ is centerless\, and we
will present our new result that $T(G)$ has to be elementary $2$-abelian
unless G satisfies some fairly strong conditions. For example\, our result
implies that T(G) is elementary $2$-abelian when $G$ is any (not necessar
ily finite) centerless perfect/almost simple/complete group.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/37/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Pavel Zalesski (University of Brasilia)
DTSTART:20210722T150000Z
DTEND:20210722T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/38
DESCRIPTION:Title: Finitely generated pro-$p$ groups acting on pro-$p$ trees\nby P
avel Zalesski (University of Brasilia) as part of GOThIC - Ischia Online G
roup Theory Conference\n\n\nAbstract\nI shall discuss various results on s
plitting of a pro-$p$ group as a free amalgamated pro-$p$ product or HNN-e
xtension in the spirit of the Bass-Serre theory of groups acting on trees.
\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/38/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Robert Guralnick (University of Southern California)
DTSTART:20211014T150000Z
DTEND:20211014T160000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/40
DESCRIPTION:Title: Topological Generation of Algebraic Groups\nby Robert Guralnick
(University of Southern California) as part of GOThIC - Ischia Online Gro
up Theory Conference\n\n\nAbstract\nWe consider the problem of generation
of (mostly simple) algebraic groups $G$ in the topological setting using t
he Zariski topology. In particular\, we will discuss the problem of how ma
ny conjugates of a given element are needed. We will give applications to
some generation problems for finite groups of Lie type and to generic stab
ilizers.\n\nThis is joint work with Tim Burness and Spencer Gerhardt.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/40/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ángel del Río (Universidad de Murcia)
DTSTART:20211021T160000Z
DTEND:20211021T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/41
DESCRIPTION:Title: A negative solution to the Modular Isomorphism Problem\nby Áng
el del Río (Universidad de Murcia) as part of GOThIC - Ischia Online Grou
p Theory Conference\n\n\nAbstract\nLet $R$ be a ring. \nThe Isomorphism Pr
oblem for group rings over $R$ asks whether the isomorphism type of a grou
p $G$ is determined by the isomorphism type of the group ring $RG$. \nThe
special case where $R$ is a field with $p$ elements and $G$ is a finite $p
$-group\, for $p$ prime\, is known as the Modular Isomorphism Problem. \n\
nThe history of the Isomorphism Problem goes back to a seminal paper of G.
Higman in the 1940s. The Modular Isomorphism Problem appeared in a survey
paper by R. Brauer in 1963. While many relevant instances of the general
Isomorphism Problem have been already resolved\, the Modular Isomorphism P
roblem resisted until now. \n\nIn cooperation with Diego García and Leo M
argolis we discovered recently two non-isomorphic groups of order $2^9$ wh
ose group algebras over any field of characteristic $2$ are isomorphic. We
will present this example and give an overview of the state of the art on
the Isomorphism Problem.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/41/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Daniele D'Angeli (Università Niccolò Cusano\, Roma))
DTSTART:20211028T160000Z
DTEND:20211028T170000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/42
DESCRIPTION:Title: Graph Automaton Groups\nby Daniele D'Angeli (Università Niccol
ò Cusano\, Roma)) as part of GOThIC - Ischia Online Group Theory Conferen
ce\n\n\nAbstract\nIn this talk I will review some basic and interesting pr
operties of automaton groups\, i.e. groups generated by the action of a tr
ansducer on a finite alphabet. Then I will explain a new construction (int
roduced in collaboration with M. Cavaleri\, A. Donno and E. Rodaro) to obt
ain automaton groups starting from finite graphs. This class of "Graph Aut
omaton groups" contains classic examples of automaton groups and other gro
ups exhibiting interesting combinatorial and spectral properties.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/42/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Michael Vaughan-Lee (Christ Church\, Oxford)
DTSTART:20211104T170000Z
DTEND:20211104T180000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/43
DESCRIPTION:Title: Schur’s exponent conjecture\nby Michael Vaughan-Lee (Christ C
hurch\, Oxford) as part of GOThIC - Ischia Online Group Theory Conference\
n\n\nAbstract\nIf $G$ is a finite group and we write $G = F/R$ where $F$ i
s a free group\,\nthen the Schur multiplier $M(G)$ is $(R \\cap F')/[F\, R
]$.\n\nThere is a long-standing conjecture attributed to I. Schur that the
exponent of $M(G)$ divides the exponent of $G$. It is easy to show that t
his is true\nfor groups $G$ of exponent $2$ or exponent $3$\, but it has b
een known since 1974\nthat the conjecture fails for exponent $4$. However
the truth or otherwise of\nthis conjecture has remained open up till now f
or groups of odd exponent.\n\nIn my talk I describe counterexamples to the
conjecture of exponent $5$\nand exponent $9$.\n\nI also give some suggest
ions for further counterexamples\, and explore the\npossibilities for alte
rnative conjectures.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/43/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Clara Franchi (Università Cattolica del Sacro Cuore\, Brescia)
DTSTART:20211111T170000Z
DTEND:20211111T180000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/44
DESCRIPTION:Title: Majorana representations of finite groups\nby Clara Franchi (Un
iversità Cattolica del Sacro Cuore\, Brescia) as part of GOThIC - Ischia
Online Group Theory Conference\n\n\nAbstract\nThe concept of Majorana repr
esentations of finite groups have been introduced by A.A. Ivanov in 2009 a
s a tool to better understand the Monster and its representation on the Co
nway-Norton-Griess algebra. \n\nIn my talk I will review the principal res
ults of the theory of Majorana representations of finite groups. In parti
cular\, I will focus on the representations of the symmetric groups\, pres
enting some joint work with A.A. Ivanov and M. Mainardis.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/44/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Alejandra Garrido (Universidad Autónoma de Madrid)
DTSTART:20211202T170000Z
DTEND:20211202T180000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/45
DESCRIPTION:Title: On various profinite completions of groups acting on rooted trees\nby Alejandra Garrido (Universidad Autónoma de Madrid) as part of GOTh
IC - Ischia Online Group Theory Conference\n\n\nAbstract\nGroups that act
faithfully on rooted trees can be studied via their finite quotients. Ther
e are several natural collections of finite quotients that can be chosen f
or this. The mathematical object that encodes all these finite quotients a
nd the maps between them is the profinite completion of the group (with re
spect to the chosen collection). Taking all possible finite quotients of t
he group gives *the* profinite completion of the group\, annd this maps on
to each of the other completions. Determining the kernels of these maps is
known as the congruence subgroup problem. This has been studied by vari
ous authors over the last few years\, most notably for self-similar groups
and (weakly) branch groups. In the case of self-similar regular branch gr
oups\, much insight can be gained into this problem using a symbolic-dynam
ical point of view. After reviewing the problem and previous work on it\,
I will report on work in progress with Zoran Sunic on determining the dyna
mical complexity of these completions and calculating some of these kernel
s with relative ease.\n\nExamples will be given. No previous knowledge of
profinite\, self-similar or branch groups is required.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/45/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Viji Thomas (Indian Institute of Science Education and Research Th
iruvananthapuram)
DTSTART:20211118T170000Z
DTEND:20211118T180000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/46
DESCRIPTION:Title: Schur’s exponent conjecture and related problems\nby Viji Tho
mas (Indian Institute of Science Education and Research Thiruvananthapuram
) as part of GOThIC - Ischia Online Group Theory Conference\n\n\nAbstract\
nAssume $G$ is a finite $p$-group\, and let $S$ be a Sylow $p$-subgroup of
$\\operatorname{Aut}(G)$ with $\\operatorname{exp}(S) = q$. We\nprove tha
t if $G$ is of class at most $p^{2} − 1$\, then $\\operatorname{exp}(G)
\\mid p^{2}\nq^{3}$\, and if $G$ is a metabelian $p$-group of class\nat mo
st $2 p − 1$\, then $\\operatorname{exp}(G) \\mid p q^{3}$. To obtain th
is result\, we will first speak about Schur’s exponent conjecture and re
lated problems. This is joint work with my PhD student P. Komma.\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/46/
END:VEVENT
BEGIN:VEVENT
SUMMARY:M. Dolores Pérez-Ramos (University of Valencia)
DTSTART:20211209T170000Z
DTEND:20211209T180000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/47
DESCRIPTION:by M. Dolores Pérez-Ramos (University of Valencia) as part of
GOThIC - Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/47/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Sandro Mattarei (University of Lincoln)
DTSTART:20211125T170000Z
DTEND:20211125T180000Z
DTSTAMP:20260404T111246Z
UID:GOThIC/48
DESCRIPTION:by Sandro Mattarei (University of Lincoln) as part of GOThIC -
Ischia Online Group Theory Conference\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/GOThIC/48/
END:VEVENT
END:VCALENDAR