On p-parts of character degrees and conjugacy class sizes of finite groups

2015/07/24 by Yang, Yong, Qian, Guohua · 1 citation
#20C15 #20C20 #20D10 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1507.06724

Abstract

Let G be a finite group and Irr(G) the set of irreducible complex characters of G. Let e_p(G) be the largest integer such that p^e_p(G) divides χ(1) for some χ∈ Irr(G). We show that |G:F(G)|_p ≤ p^{k e_p(G)} for a constant k. This settles a conjecture of A. Moretó. We also study the related problems of the p-parts of conjugacy class sizes 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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