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SUMMARY:Zeinab Akhlaghi (Amirkabir University of technology (Iran))
DTSTART:20210226T143000Z
DTEND:20210226T151500Z
DTSTAMP:20260404T131148Z
UID:FGV/1
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/FGV/1
 /">Character degree graph and Huppert’s ρ-σ- conjecture</a>\nby Zeinab
  Akhlaghi (Amirkabir University of technology (Iran)) as part of Finite Gr
 oups in Valencia\n\n\nAbstract\nCharacter Theory is one of the strong tool
 s in the theory of finite groups\, and\, given a finite group $G$ the stud
 y of the set $\\mathrm {cd}(G)=\\{\\\,\\theta(1)\\\,|\\\,\\theta\\in \\mat
 hrm{ Irr}(G)\\}$\, of all degrees of the irreducible complex characters of
  $G$\, has an important role in finite group theory.  Associating a graph 
 to the degree-set is one of the method to approach this set.  The characte
 r degree graph $\\Delta(G)$ is  defined as the graph whose vertex set is t
 he set of all the prime numbers that divide some $\\theta(1)\\in \\mathrm{
 cd}(G)$\, while a pair $(p\,q)$ of distinct vertices $p$ and $q$ belongs t
 o the edge set if and only if $pq$ divides an element in $\\mathrm{cd}(G)$
 . So far\, many studies have been done on this graph. In this talk\, we wi
 ll discuss the recent development obtained on this graph and finally focus
  on a new result on Huppert’s $\\rho-\\sigma$  conjecture\, which is der
 ived from the recent development on this graph.\n
LOCATION:https://stable.researchseminars.org/talk/FGV/1/
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