A variant of a theorem of J. A. Green
type: Item
instance of: scholarly article
title: A variant of a theorem of J. A. Green
zbMATH Open document ID: 0606.20014
DOI: 10.1016/0021-8693(86)90239-5
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: A classical theorem of \textit{J. A. Green} [Math. Z. 70, 430-445 (1959; Zbl 0086.024)] asserts that for a given finite group G with a normal subgroup N such that G/N is a p-group, and an absolutely indecomposable KN-module V, where K is a field of characteristic p, the induced module \(V^ G\) is absolutely indecomposable. The present article studies a similar situation without assuming V to be absolutely indecomposable. Theorem: Let K be a perfect field with characteristic \(p>0\), let \(N\trianglelefteq G\) and let V be an indecomposable KN-module whose inertia group modulo N is a p-group. Then all indecomposable components of \(V^ G\) are isomorphic. An elementary example \((K=GF(2)\), \(G=\Sigma_ 3\), \(N=A_ 3)\) is given showing that \(V^ G\) need not be indecomposable.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20D15
zbMATH DE Number: 3979339
zbMATH Keywords: absolutely indecomposable
zbMATH Keywords: induced module
zbMATH Keywords: inertia group
zbMATH Keywords: indecomposable components
author: Morton E. Harris
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90239-5
OpenAlex ID: W2071539595
cites work: Q3955560
cites work: Q3934684
cites work: Sur l'induction des modules indécomposables et la projectivité rélative
description: scientific article; zbMATH DE number 3979339