Components of induced modules
type: Item
instance of: scholarly article
title: Components of induced modules
zbMATH Open document ID: 0546.20009
DOI: 10.1016/0021-8693(84)90151-0
author: David W. Burry
published in: Journal of Algebra
publication date: 1984-01-01T00:00:00Z
review text: The paper deals with various aspects of the Green correspondence. The interested leader should consult the paper for details. We note, however, that Theorem 4.3 is not quite correct as it stands. A revised version, suggested by the author, should read as follows: Let p be a prime and H a subgroup of the finite group G. Denote by \({\mathcal L}\) the set of p-subgroups P of H such that \(N_ G(P)\subseteq H\) and by \({\mathcal N}\) the set of p-subgroups P of H such that \(N_ G(P)\not\subseteq H\). (1) For any indecomposable H-module U with its vertices in \({\mathcal L}\), \(U^ G=V\oplus X\) where V is indecomposable with a vertex in \({\mathcal L}\) and every component of X has a vertex in \({\mathcal N}\). (2) For any indecomposable G-module V with a vertex P in \({\mathcal L}\), let \(P_ 1=P,P_ 2,...,P_ r,...,P_ n\) be representatives of each H- conjugacy class fused to P in G with \(P_ 1,...,P_ r\) the ones in \({\mathcal L}\). Then \(V_ H=W_ 1\oplus...\oplus W_ n\oplus Y\) where \(W_ i\) is indecomposable with vertex \(P_ i\) for \(i=1,...,r\), every component of \(W_ i\) has vertex \(P_ i\) for \(i=r+1,...,n\) and every component of Y has its vertices in \({\mathcal N}\). (3) For U an indecomposable H-module with vertices in \({\mathcal L}\), \(V| U^ G\) if and only if \(U| V_ H\).
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 3869572
zbMATH Keywords: Green correspondence
zbMATH Keywords: p-subgroups
zbMATH Keywords: vertices
zbMATH Keywords: indecomposable G-module
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: 0021-8693(84)90151-0
OpenAlex ID: W1991752025
cites work: Block theory with modules
cites work: A strengthened theory of vertices and sources
cites work: Restrictions of Modules to Local Subgroups
cites work: Q3955560
cites work: Pointed groups and construction of characters
cites work: Modular Permutation Representations
description: scientific article; zbMATH DE number 3869572