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Corpus ID: 249953633

Variations on average character degrees and solvability

@inproceedings{Ahanjideh2022VariationsOA,
title={Variations on average character degrees and solvability},
author={Neda Ahanjideh and Zeinab Akhlaghi and Kamal Aziziheris},
year={2022}
}

. Let G be a ﬁnite group, F be one of the ﬁelds Q , R or C , and N be a non-trivial normal subgroup of G . Let acd ∗ F ( G ) and acd F ,even ( G | N ) be the average degree of all non-linear F -valued irreducible characters of G and of even degree F -valued irreducible characters of G whose kernels do not contain N , respectively. We assume the average of an empty set is 0 for more convenience. In this paper we prove that if acd ∗ Q ( G ) < 9 / 2 or 0 < acd Q ,even ( G | N ) < 4, then G is… Expand

We prove that if the average of the degrees of the irreducible characters of a finite group G is less than 165 , then G is solvable. This solves a conjecture of I. M. Isaacs, M. Loukaki and the first… Expand

We study finite groups whose rational-valued irreducible characters are all of odd degrees. We conjecture that in such groups, all rational elements must be 2-elements.

Let G(q) be a finite simple group of Lie type over a finite field of order q and d(G(q)) the minimal degree of faithful projective complex representations of G(q). For the case G(q) is a classical… Expand

Given a finite group G, we write acd(G) to denote the average of the degrees of the irreducible characters of G. We show that if acd(G) ≤ 3, then G is solvable. Also, if acd(G) < 3/2, then G is… Expand