Clifford theory for semisimple \(G\)-groups
type: Item
instance of: scholarly article
title: Clifford theory for semisimple \(G\)-groups
zbMATH Open document ID: 0976.20004
published in: Journal of Algebra
publication date: 2001-09-18T00:00:00Z
review text: Let \(G\) be a finite group, \(H\) a subgroup of \(G\), and \(A\) a group acted on by \(H\). \(A\) is said to be an irreducible \(H\)-group if it has no non-trivial proper normal \(H\)-invariant subgroups, and \(A\) is semisimple if it is a direct product of non-Abelian irreducible \(H\)-groups. Starting with this concept, the authors define a based \(G\)-functor, and using the results of the previous paper [J. Algebra 231, No. 2, 601-613 (2000; see the preceding review Zbl 0976.20003)], they prove the existence of a Clifford theory for this \(G\)-functor.
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 20C15
Mathematics Subject Classification ID: 20C20
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 19A22
zbMATH DE Number: 1526426
zbMATH Keywords: based \(G\)-functors
zbMATH Keywords: Clifford theory
zbMATH Keywords: non-Abelian \(G\)-groups
zbMATH Keywords: finite groups
author: Julio P. Lafuente
author: Inmaculada Lizasoain
author: Gustavo Ochoa
MaRDI profile type: Publication
full work available at URL: jabr.2000.8336
OpenAlex ID: W2079226536
cites work: Representations induced in an invariant subgroup
cites work: Axiomatic representation threory for finite groups
cites work: On complemented nonabelian chief factors of a finite group
cites work: Projective \(G\)-groups
cites work: Théoremes de finitude en cohomologie galoisienne
DOI: 10.1006/JABR.2000.8336
description: scientific article; zbMATH DE number 1526426