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

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.

Publication Details

Journal
ArXiv.org
Published
2025-03-10
Primary Topic
Finite Group Theory Research
Type
article
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article

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

ArXiv.org
Finite Group Theory Research
article

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

article en

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.

ArXiv.org
Openalex Percentile: Top 42%
Finite Group Theory Research
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$M$-groups and Codegrees; $M_{p}$-groups and Brauer Character Degrees · ArXiv.org (2025) | TGRS Research Map | TGRS