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Journal of Algebra
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Journal of Algebra
Article . 2006
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Factorisations of sporadic simple groups

Factorisations of sporadic simple groups.
Authors: Giudici, Michael;

Factorisations of sporadic simple groups

Abstract

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.

Keywords

Algebra and Number Theory, Products of subgroups of abstract finite groups, sporadic simple groups, group factorizations, Group factorisations, Sporadic simple groups, Simple groups: sporadic groups, exact factorizations

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
30
Top 10%
Top 10%
Top 10%
hybrid