Problems on characters involving two primes

Abstract: In the first part of the talk we will see that if $G$ is a nontrivial finite group, then for every pair of primes $\{p,q\}$ there is some nontrivial irreducible character of $G$ whose degree is not divisible by $p$ nor $q$. This result will allow us to characterize groups in which all irreducible characters of degree not divisible by $p$ nor $q$ are linear. In the second part of my talk, I will discuss on what can be said about the field of values of such a character of $\{p, q\}$'-degree. This talk is based in joint works with E Giannelli, N. Hung and M. Schaeffer Fry.

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