On projective summands of induced modules
type: Item
instance of: scholarly article
title: On projective summands of induced modules
zbMATH Open document ID: 0675.20004
DOI: 10.1016/0021-8693(89)90240-8
author: Geoffrey R. Robinson
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let F be an algebraically closed field of prime characteristic p, let G be a finite group, and let H be a subgroup of G. Using the Reynolds ideal, the author proves the following reciprocity theorem: If S is a simple FG-module with projective cover P, and if T is a simple FH-module with projective cover Q then the multiplicity of Q as a direct summand of \(Res^ G_ H(S)\) coincides with the multiplicity of P as a direct summand of \(Ind^ G_ H(T)\). This result is then applied to bound Cartan invariants and dimensions of projective modules.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 16S34
Mathematics Subject Classification ID: 20C20
zbMATH DE Number: 4105196
zbMATH Keywords: finite group
zbMATH Keywords: Reynolds ideal
zbMATH Keywords: reciprocity theorem
zbMATH Keywords: simple FG-module
zbMATH Keywords: projective cover
zbMATH Keywords: multiplicity
zbMATH Keywords: direct summand
zbMATH Keywords: Cartan invariants
zbMATH Keywords: projective modules
reviewed by: Burkhard Külshammer
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90240-8
OpenAlex ID: W2042445202
cites work: Bilinear forms on G-algebras
cites work: Remarks on the group algebra as symmetric algebra.
cites work: The modular Hecke algebra of a Sylow p-subgroup
description: scientific article; zbMATH DE number 4105196