PERMUTABLE DIAGONAL-TYPE SUBGROUPS OF G*H

Two subgroups M and S of a group G are said to permute, or M permutes with S, if MS = SM. Furthermore, M is a permutable subgroup of G if M permutes with every subgroup of G. In this article, we provide necessary and sufficient conditions for a subgroup of G* H, whose intersections with the direct factors are normal, to be a permutable subgroup.