Factorisations of sporadic simple groups.
type: Item
instance of: scholarly article
title: Factorisations of sporadic simple groups.
zbMATH Open document ID: 1107.20019
author: Michael Giudici
published in: Journal of Algebra
publication date: 2006-12-07T00:00:00Z
review text: A group \(G\) is called factorizable if there exist proper subgroups \(A\) and \(B \) of \(G\) such that \(G=AB\). The factorization is called exact if \(A\cap B=1\) is the trivial group. Recently factorizations of finite groups have attracted attention of mathematicians so that we mention a few research works. \textit{J. Wiegold} and \textit{A. G. Williamson} [in Math. Z. 175, 171-179 (1980; Zbl 0424.20004)], found all the exact factorizations of the alternating and the symmetric groups. \textit{G. L. Walls} [in Arch. Math. 53, No. 3, 209-216 (1989; Zbl 0652.20027)], found all the factorizations of the alternating and the symmetric groups with both factors simple. The reviewer [in \textit{M. R. Darafsheh, G. R. Rezaeezadeh} and \textit{G. L. Walls}, Algebra Colloq. 10, No. 2, 195-204 (2003; Zbl 1038.20013)], determined the structure of a finite factorizable group with one factor a non-Abelian simple group and the other factor isomorphic to the symmetric group on \(6\) letters. \textit{T. R. Gentchev} [Arch. Math. 47, 97-102 (1986; Zbl 0578.20008)] found factorizations of all the sporadic simple groups as the product of two simple groups. In the paper under review the author determines all the factorizations of the \(26\) sporadic simple groups and their automorphism groups.
Mathematics Subject Classification ID: 20D40
Mathematics Subject Classification ID: 20D08
zbMATH DE Number: 5078827
zbMATH Keywords: group factorizations
zbMATH Keywords: sporadic simple groups
zbMATH Keywords: exact factorizations
reviewed by: M. R. Darafsheh
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2006.04.019
OpenAlex ID: W2006794563
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DOI: 10.1016/J.JALGEBRA.2006.04.019
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description: scientific article; zbMATH DE number 5078827