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

authored by

Christine Bessenrodt, Yong Yang

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^ke¯_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.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

Texas State University
Chongqing University of Arts and Science

Type

Article

Journal

Journal of algebra

Volume

560

Pages

296-311

No. of pages

16

ISSN

0021-8693

Publication date

15.10.2020

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Algebra and Number Theory

Electronic version(s)

https://doi.org/10.1016/j.jalgebra.2020.05.018 (Access: Closed)