Mutually permutable products of finite groups
Let the finite group \(G=HK\) be the product of two subgroups \(H\) and \(K\) such that \(H\) permutes with every subgroup of \(K\) and \(K\) permutes with every subgroup of \(H\). It is shown that if \(K\) is nilpotent or if \(K\) is supersoluble and the commutator subgroup of \(G\) is nilpotent, then the supersoluble residuals of \(G\) and \(H\) coincide.
scientific article; zbMATH DE number 1270887