Character degree graph and Huppert’s ρ-σ- conjecture

Abstract: Character Theory is one of the strong tools in the theory of finite groups, and, given a finite group $G$ the study of the set $\mathrm {cd}(G)=\{\,\theta(1)\,|\,\theta\in \mathrm{ Irr}(G)\}$, 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 character degree 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 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 will discuss the recent development obtained on this graph and finally focus on a new result on Huppert’s $\rho-\sigma$ conjecture, which is derived from the recent development on this graph.

group theory

Audience: researchers in the topic

Finite Groups in Valencia

Series comments: The seminar meets weekly from February 26th to March 30th 2021.

For a detailed schedule and registration details, please visit the seminar webpage at

sites.google.com/view/finite-groups-seminar2021