Factorisations of sporadic simple groups.
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.
scientific article; zbMATH DE number 5078827
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