Factorisations of characteristically simple groups
A group factorization is a pair \((G,\{A,B\})\) where \(G\) is a group and \(A\), \(B\) are subgroups such that \(AB=G\). The factorization is nontrivial if \(A\neq G\neq B\). Such a factorization is a full factorization if \(|G|\), \(|A|\) and \(|B|\) are divisible by the same primes. In [J. Algebra 204, No. 1, 129-187 (1998; Zbl 0907.20033)] \textit{R. W. Baddeley} and \textit{C. E. Praeger} described all full factorizations \((T,\{A,B\})\) for finite simple groups \(T\). The investigations of [``Permutation groups preserving Cartesian decompositions'', in preparation] let \textit{R. W. Baddeley}, \textit{C. E. Praeger} and \textit{C. Schneider} to the question of full factorizations of characteristically simple groups. In the paper under review the authors determine these factorizations. They also obtain a result on strong multiple factorizations of characteristically simple groups which generalizes the corresponding result on simple groups in the paper of Baddeley and Praeger.
scientific article; zbMATH DE number 1868000