Non-simple groups which are the product of simple groups
type: Item
instance of: scholarly article
title: Non-simple groups which are the product of simple groups
zbMATH Open document ID: 0652.20027
DOI: 10.1007/BF01277053
published in: Archiv der Mathematik
publication date: 1989-01-01T00:00:00Z
review text: This paper investigates the structure of groups with non-trivial center which can be written as a product of two simple subgroups. Examples must be covering groups of simple groups. For example \(2\cdot PSU(4,3)=AB\) where \(A\simeq PSp(4,3)\) and \(B\simeq PSL(4,3)\) and \(3\cdot PSU(4,3)=AB\) where \(A\simeq PSp(4,3)\) and \(B\simeq PSU(3,3).\) The main results of the paper include the fact that no covering group of an alternating group can be written as a product of two simple subgroups. The fact that if \(G=AB\) where A and B are simple subgroups with G/N a sporadic simple group for some normal subgroup N of G, then either \(G\simeq A\times B\), \(N=1\) and G is a simple group, (all these factorizations are known), or \(| N| =3\) and G/N\(\simeq Suz\), \(A\simeq PSU(5,2)\) and \(B\simeq G_ 2(4)\). A similar result is proven when G/N is a group of Lie type 1 or 2 and N is the center of G and has prime order. In this case there are several possibilities.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D05
Mathematics Subject Classification ID: 20D30
zbMATH DE Number: 4063365
zbMATH Keywords: groups with non-trivial center
zbMATH Keywords: product of two simple subgroups
zbMATH Keywords: covering groups of simple groups
zbMATH Keywords: sporadic simple group
zbMATH Keywords: group of Lie type
author: G. L. Walls
MaRDI profile type: Publication
cites work: Q3746007
cites work: Finite Permutation Groups and Finite Simple Groups
cites work: Q3684278
cites work: On subgroups of.O. II. Local structure
cites work: Factorizations of the groups of Lie type of Lie rank 1 or 2
cites work: Factorizations of the sporadic simple groups
cites work: Q3748464
cites work: Products of simple groups
cites work: Factorizations of finite groups
cites work: Products of \(A_5\) and a finite simple group
cites work: Products of finite simple groups
cites work: Groups which are the products of simple groups
cites work: The maximal subgroups of Conway's group \(Co_ 1\)
cites work: The complex Leech lattice and maximal subgroups of the Suzuki group
full work available at URL: https://doi.org/10.1007/bf01277053
OpenAlex ID: W2017980557
description: scientific article; zbMATH DE number 4063365