On minimal non \(M_ p\)-groups
type: Item
instance of: scholarly article
title: On minimal non \(M_ p\)-groups
zbMATH Open document ID: 0783.20009
DOI: 10.1007/BF01207184
published in: Archiv der Mathematik
publication date: 1993-11-15T00:00:00Z
review text: We study the structure of minimal non \(M_ p\)-groups. A finite group \(G\) is called an \(M_ p\)-group if every irreducible \(FG\)-module is monomial, where \(F\) is an algebraically closed field of characteristic \(p>2\). This is a \(p\)-modular analogue of the definition of \(M\)-groups. The structure of minimal non \(M\)-groups was studied by \textit{D. T. Price} [Math. Z. 130, 325-337 (1973; Zbl 0241.20007)], and using it, we obtain the similar result for minimal non \(M_ p\)-groups. Also we prove that some minimal non \(M_ p\)-groups cannot be normal subgroups of \(M_ p\)-groups.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 446303
zbMATH Keywords: minimal non \(M_ p\)-groups
zbMATH Keywords: finite group
zbMATH Keywords: irreducible \(FG\)-module
author: Akihide Hanaki
MaRDI profile type: Publication
cites work: Q3481923
cites work: Endliche Gruppen I
cites work: Q4103728
cites work: Primitive characters, normal subgroups, and M-groups
cites work: Q3826736
cites work: Module correspondence in finite groups
cites work: Q3037646
full work available at URL: https://doi.org/10.1007/bf01207184
OpenAlex ID: W1982994494
description: scientific article; zbMATH DE number 446303