The average character degree of finite groups and Gluck's conjecture

2022/09/19 by Moretó, Alexander
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2209.09279

Abstract

We prove that the order of a finite group G with trivial solvable radical is bounded above in terms of \rm acd(G), the average degree of the irreducible characters. It is not true that the index of the Fitting subgroup is bounded above in terms of \rm acd(G), but we show that in certain cases it is bounded in terms of the degrees of the irreducible characters of G that lie over a linear character of the Fitting subgroup. This leads us to propose a refined version of Gluck's conjecture.

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