A remark on p-radical groups
type: Item
instance of: scholarly article
title: A remark on p-radical groups
zbMATH Open document ID: 0713.20004
DOI: 10.1016/0021-8693(90)90063-T
author: Shigeo Koshitani
published in: Journal of Algebra
publication date: 1990-01-01T00:00:00Z
review text: Let FG be the group algebra of a finite group G over an algebraically closed field F of characteristic \(p>0\). Let P be a p-Sylow subgroup of G. Following \textit{K. Motose} and \textit{Y. Ninomiya} [Math. J. Okayama Univ. 17, 171-176 (1975; Zbl 0316.20004)], G is said to be p-radical if the induced module \((F_ P)^ G\) from the trivial FP-module \(F_ P\) is a direct sum of simple FG-modules. \textit{T. Okuyama} proved that a p-radical group is p-soluble [Hokkaido Math. J. 10, 299-318 (1981; Zbl 0488.20013)]. The author derives a useful sufficient condition that G should be p-radical, namely that for any simple FG-module S whose vertex is Q the restriction to \(F[N_ G(Q)]\) should be a simple \(F[N_ G(Q)]\)- module.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 4173217
zbMATH Keywords: group algebra
zbMATH Keywords: finite group
zbMATH Keywords: p-Sylow subgroup
zbMATH Keywords: induced module
zbMATH Keywords: direct sum of simple FG-modules
zbMATH Keywords: p-radical group
zbMATH Keywords: p-soluble
zbMATH Keywords: vertex
MaRDI profile type: Publication
cites work: Q3804896
cites work: Q3955560
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full work available at URL: 0021-8693(90)90063-t
OpenAlex ID: W2072361060
description: scientific article; zbMATH DE number 4173217