On Huppert’s $\rho-\sigma$ conjecture

Abstract: The set of the degrees of the irreducible complex characters of a finite group $G$ has been an object of considerable interest since the second part of the 20th century, and the study of the arithmetical structure of this set is a particularly intriguing aspect of Character Theory of finite groups. A remarkable question in this research area was posed by B. Huppert in the 80’s: is it true that at least one of the character degrees is divisible by a ”large” portion of the entire set of primes that appear as divisors of some character degree? More precisely, denoting by $\rho(G)$ the set of primes that divide some character degree, and by $\sigma(G)$ the largest number of primes that divide a single character degree, Huppert’s $\rho-\sigma$ conjecture predicts that $|\rho(G)| ≤ 3\sigma(G)$ holds for every finite group G, and that $|\rho(G)| ≤ 2\sigma(G)$ if $G$ is solvable. In this talk we will discuss some recent developments in the study of Huppert’s conjecture, obtained in a joint work with Z. Akhlaghi and S. Dolfi.

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