p-radical groups are p-solvable
type: Item
instance of: scholarly article
title: p-radical groups are p-solvable
zbMATH Open document ID: 0611.20006
author: Tetsuro Okuyama
published in: Osaka Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Let k be an algebraically closed field of characteristic \(p>0\), G a finite group with Sylow p-subgroup P, and \(k_ P\) the trivial kP-module. G is called p-radical if \(k^ G_ P\) is completely reducible. It is shown that if G is p-radical then G is p-solvable. Furthermore if G is p- radical with Sylow p-subgroup P and \(D=P\cap P^ x\), then D is a vertex of some simple kG-module if \(x\in G\) and D is a defect group of some p- block of G if \(x\in C_ G(D)\).
reviewed by: B.G.Basmaji
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 3987540
zbMATH Keywords: finite group
zbMATH Keywords: Sylow p-subgroup
zbMATH Keywords: completely reducible
zbMATH Keywords: p-radical
zbMATH Keywords: p- solvable
zbMATH Keywords: vertex
zbMATH Keywords: defect group
zbMATH Keywords: p-block
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3987540