$M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees

Xiaoyou Chen; Mark L. Lewis

$M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees

Group Theory 2025-03-11 v1

Authors: Xiaoyou Chen , Mark L. Lewis

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 every 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

finite groups character theory finite group theory

Cite

@article{arxiv.2503.06878,
  title  = {$M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees},
  author = {Xiaoyou Chen and Mark L. Lewis},
  journal= {arXiv preprint arXiv:2503.06878},
  year   = {2025}
}

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