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

Yong Yang; Guohua Qian

paper

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

arXiv:1507.06724

Abstract

Let $G$ be a finite group and $I r r (G)$ 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 $χ \in I r r (G)$ . We show that $∣ G : F (G) ∣_{p} \leq p^{k e_{p} (G)}$ 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.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1501.03237