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$M_{p}$-GROUPS AND BRAUER CHARACTER DEGREES

Part of: Representation theory of groups

Published online by Cambridge University Press:  09 May 2025

XIAOYOU CHEN Open the ORCID record for XIAOYOU CHEN [Opens in a new window]  and
MARK L. LEWIS Open the ORCID record for MARK L. LEWIS [Opens in a new window]
XIAOYOU CHEN
Affiliation:
School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, PR China e-mail: [email protected]
MARK L. LEWIS*
Affiliation:
Department of Mathematical Sciences, Kent State University, Kent, OH 44242, USA
*
e-mail: [email protected]
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Abstract

Let G be a finite group and p be a prime. We prove that if G has three codegrees, then G is an M-group. We prove for some prime p that if the degree of every nonlinear irreducible Brauer character of G is a prime, then for every normal subgroup N of G, either $G/N$ or N is an $M_p$-group.

Keywords

Brauer charactercodegreeM-groupMp-group

MSC classification

Primary: 20C15: Ordinary representations and characters
Secondary: 20C20: Modular representations and characters
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 5
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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Footnotes

The first author is grateful for the support of the China Scholarship Council and the International Training Program of Henan Province, the programs of Henan University of Technology (2024PYJH019 and HNGD2024020), the projects of Education Department of Henan Province (23A110010, YJS2022JC16), and the Natural Science Foundation of Henan Province (242300421384).

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