Factorisations of characteristically simple groups
type: Item
instance of: scholarly article
title: Factorisations of characteristically simple groups
zbMATH Open document ID: 1014.20012
DOI: 10.1016/S0021-8693(02)00111-4
author: Cheryl E. Praeger
author: Csaba Schneider
published in: Journal of Algebra
publication date: 2003-02-12T00:00:00Z
review text: A group factorization is a pair \((G,\{A,B\})\) where \(G\) is a group and \(A\), \(B\) are subgroups such that \(AB=G\). The factorization is nontrivial if \(A\neq G\neq B\). Such a factorization is a full factorization if \(|G|\), \(|A|\) and \(|B|\) are divisible by the same primes. In [J. Algebra 204, No. 1, 129-187 (1998; Zbl 0907.20033)] \textit{R. W. Baddeley} and \textit{C. E. Praeger} described all full factorizations \((T,\{A,B\})\) for finite simple groups \(T\). The investigations of [``Permutation groups preserving Cartesian decompositions'', in preparation] let \textit{R. W. Baddeley}, \textit{C. E. Praeger} and \textit{C. Schneider} to the question of full factorizations of characteristically simple groups. In the paper under review the authors determine these factorizations. They also obtain a result on strong multiple factorizations of characteristically simple groups which generalizes the corresponding result on simple groups in the paper of Baddeley and Praeger.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 1868000
zbMATH Keywords: group factorizations
zbMATH Keywords: full factorizations
zbMATH Keywords: finite simple groups
zbMATH Keywords: characteristically simple groups
zbMATH Keywords: strong multiple factorizations
Wikidata QID: Q56987936
reviewed by: Ulrich Dempwolff
MaRDI profile type: Publication
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full work available at URL: s0021-8693(02)00111-4
OpenAlex ID: W2056068109
description: scientific article; zbMATH DE number 1868000