Groups which are the products of simple groups
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.
scientific article; zbMATH DE number 3987551