A Green ring version of the Brauer induction theorem
type: Item
instance of: scholarly article
title: A Green ring version of the Brauer induction theorem
zbMATH Open document ID: 0627.20004
DOI: 10.1016/0021-8693(87)90235-3
author: Peter Sin
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: Let F be an algebraically closed field of prime characteristic p, let G be a finite group, let V be a fixed p-subgroup of G, and let E(V) be the set of all subgroups H of G such that \(O_ p(H)\leq V\) and \(H/O_ p(H)\) is elementary. The author shows that, in the Green ring of G, any V- projective FG-module is a \({\mathbb{Z}}\)-linear combination of modules induced from subgroups in E(V). Moreover, he proves that E(V) is in some sense minimal with this property. There are similar results with a valuation ring replacing the field F.
reviewed by: Burkhard Külshammer
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 16E20
zbMATH DE Number: 4019305
zbMATH Keywords: induction theorem
zbMATH Keywords: vertex
zbMATH Keywords: relative projectivity
zbMATH Keywords: Grothendieck ring
zbMATH Keywords: defect base
zbMATH Keywords: finite group
zbMATH Keywords: p-subgroup
zbMATH Keywords: Green ring
zbMATH Keywords: projective FG-module
zbMATH Keywords: modules induced from subgroups
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90235-3
OpenAlex ID: W2014642095
cites work: The Green Correspondence and Brauer's Characterization of Characters
cites work: Sur l'induction des modules indécomposables et la projectivité rélative
cites work: Structure in representation algebras
cites work: Q5829823
cites work: Axiomatic representation threory for finite groups
description: scientific article; zbMATH DE number 4019305