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

Yong Yang; Guohua Qian

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arXiv · 1507.06724

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

Yong Yang·Guohua Qian

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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 $\chi(1)$ for some $\chi \in Irr(G)$. We show that $|G:\mathbf{F}(G)|_p \leq p^{k e_p(G)}$ for a constant $k$. This settles a conjecture of A. Moret\'o. We also study the related problems of the $p$-parts of conjugacy class sizes of finite groups.

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Yong Yang, Guohua Qian. 2015-07-24. On p-parts of character degrees and conjugacy class sizes of finite groups. https://arxiv.org/abs/1507.06724

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