Bounding p-Brauer characters in finite groups with two conjugacy classes of p-elements

authored by

Nguyen Ngoc Hung, Benjamin Sambale, Pham Huu Tiep

Abstract

Let k(B_0) and l(B_0) respectively denote the number of ordinary and p-Brauer irreducible characters in the principal block B_0 of a finite group G. We prove that, if k(B_0)-l(B_0)=1, then l(B_0)\geq p-1 or else p=11 and l(B_0)=9. This follows from a more general result that for every finite group G in which all non-trivial p-elements are conjugate, l(B_0)\geq p-1 or else p = 11 and G/O_{p'}(G) =11^2:SL(2,5). These results are useful in the study of principal blocks with a few characters. We propose that, in every finite group G of order divisible by p, the number of irreducible Brauer characters in the principal p-block of G is always at least 2\sqrt{p-1}+1-k_p(G), where k_p(G) is the number of conjugacy classes of p-elements of G. This indeed is a consequence of the celebrated Alperin weight conjecture and known results on bounding the number of p-regular classes in finite groups.

Organisation(s)

Institute of Algebra, Number Theory and Discrete Mathematics

External Organisation(s)

University of Akron
Rutgers University

Type

Article

Journal

Israel Journal of Mathematics

Volume

262

Pages

327–358

No. of pages

32

ISSN

0021-2172

Publication date

09.2024

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

General Mathematics

Electronic version(s)

http://arxiv.org/abs/2102.04443v2 (Access: Open)
https://doi.org/10.1007/s11856-024-2613-1 (Access: Open)