On p-parts of Brauer character degrees and p-regular conjugacy class sizes

2018/04/23 by Bessenrodt, Christine, Yang, Yong · 1 citation
#20C15 #20C20 #20D10 #20D20 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1804.08241

Abstract

Let G be a finite group, p a prime, and IBr_p(G) the set of irreducible p-Brauer characters of G. Let e_p(G) be the largest integer such that p ^e_p(G) divides χ(1) for some χ∈ IBr_p(G). We show that |G:O_p(G)|_p ≤ p^{k e_p(G)} for an explicitly given constant k. We also study the analogous problem for the p-parts of the conjugacy class sizes of p-regular elements of finite groups.

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• On p-parts of conjugacy class sizes and the index of the p-core

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