Groups which are the products of simple groups
type: Item
instance of: scholarly article
title: Groups which are the products of simple groups
zbMATH Open document ID: 0611.20017
DOI: 10.1007/BF01313486
published in: Archiv der Mathematik
publication date: 1988-01-01T00:00:00Z
review text: This paper is a continuation of the study of groups which can be written as the product of two simple subgroups. The main result is that if a finite group \(G=AB=AN\) where A, B are simple subgroups of G and N is a normal subgroup of G, then (i) \(G\cong A\times B\), (ii) \(G=A\), or (iii) A,B\(\cong GL(2,3)\) and \(G=Hol(Z_ 2\times Z_ 2\times Z_ 2).\) Also, the paper determines which groups \(G=AB\) where A, B are simple groups and are such that there exists a prime p so that \(p| | A|\) and \(2p>[B: A\cap B]\). The possible groups are basically, the groups in the above theorem and various alternating and Mathieu groups. The classification of all simple groups was used.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D05
zbMATH DE Number: 3987551
zbMATH Keywords: product of two simple subgroups
author: G. L. Walls
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3987551