A note on the Green invariants in finite group modular representative theory.
type: Item
instance of: scholarly article
title: A note on the Green invariants in finite group modular representative theory.
zbMATH Open document ID: 1145.20006
published in: Results in Mathematics
publication date: 2008-06-10T00:00:00Z
review text: Let \(\mathcal O\) be a complete Noetherian local commutative ring with algebraically closed residue field \(k\), and let \(N\) be a normal subgroup of a finite group \(G\). For an indecomposable \(\mathcal O[G/N]\)-module \(V\) and its inflation \(\widehat V\) to \(G\), the author relates the vertices, sources and Green correspondents of \(V\) and \(\widehat V\). Let \(W,X\) be \(\mathcal OG\)-modules such that \(W\otimes_{\mathcal O}X\) is indecomposable, and suppose that the restriction of \(W\) to a Sylow \(p\)-subgroup of \(G\) is a capped endo-permutation module. The author relates the vertices, sources and Green correspondents of \(X\) and \(W\otimes_{\mathcal O}X\). Reviewer's remark: The title of the paper should probably read ``A note on the Green invariants in finite group modular representation theory''.
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
zbMATH DE Number: 5285867
zbMATH Keywords: vertices
zbMATH Keywords: sources
zbMATH Keywords: Green correspondence
zbMATH Keywords: endo-permutation modules
zbMATH Keywords: Green invariants
author: Morton E. Harris
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: s00025-007-0274-0
OpenAlex ID: W2069223860
DOI: 10.1007/S00025-007-0274-0
description: scientific article; zbMATH DE number 5285867