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arXiv · 2503.06878

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

Xiaoyou Chen·Mark L. Lewis
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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 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.

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Xiaoyou Chen, Mark L. Lewis. 2025-03-10. $M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees. https://arxiv.org/abs/2503.06878

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