On the first cohomology of a group with coefficients in a simple module
type: Item
instance of: scholarly article
title: On the first cohomology of a group with coefficients in a simple module
zbMATH Open document ID: 0593.20061
DOI: 10.1016/0021-8693(86)90043-8
author: L. G. Kovács
author: R. B. Howlett
published in: Journal of Algebra
publication date: 1986-01-01T00:00:00Z
review text: The authors give a proof of the following result. Let k be a field and let N be a subnormal subgroup of the group G. If V is a simple kG-module and if U is a simple kN-module of V on which N acts nontrivially, then one has dim \(H^ 1(G,V)\leq \dim H^ 1(N,U)\). This improves a result of \textit{M. Aschbacher} and \textit{L. Scott} [J. Algebra 92, 44-80 (1985; Zbl 0549.20011)].
reviewed by: Urs Stammbach
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20C07
Mathematics Subject Classification ID: 20E15
Mathematics Subject Classification ID: 20D25
zbMATH DE Number: 3953095
zbMATH Keywords: first cohomology
zbMATH Keywords: subnormal subgroup
zbMATH Keywords: simple kG-module
MaRDI profile type: Publication
full work available at URL: 0021-8693(86)90043-8
OpenAlex ID: W2053152886
cites work: Maximal subgroups of finite groups
cites work: Q3856855
description: scientific article; zbMATH DE number 3953095