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SUMMARY:Zeinab Akhlaghi (Amirkabir University of technology (Iran))
DTSTART:20210226T143000Z
DTEND:20210226T151500Z
DTSTAMP:20260423T021725Z
UID:FGV/1
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/FGV/1/">Char
 acter degree graph and Huppert’s ρ-σ- conjecture</a>\nby Zeinab Akhlag
 hi (Amirkabir University of technology (Iran)) as part of Finite Groups in
  Valencia\n\n\nAbstract\nCharacter Theory is one of the strong tools in th
 e theory of finite groups\, and\, given a finite group $G$ the study of th
 e set $\\mathrm {cd}(G)=\\{\\\,\\theta(1)\\\,|\\\,\\theta\\in \\mathrm{ Ir
 r}(G)\\}$\, 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 character degre
 e graph $\\Delta(G)$ is  defined as the graph whose vertex set is the 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 to the e
 dge set if and only if $pq$ divides an element in $\\mathrm{cd}(G)$. So fa
 r\, many studies have been done on this graph. In this talk\, we will disc
 uss the recent development obtained on this graph and finally focus on a n
 ew result on Huppert’s $\\rho-\\sigma$  conjecture\, which is derived fr
 om the recent development on this graph.\n
LOCATION:https://researchseminars.org/talk/FGV/1/
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