Totally permutable products of certain classes of finite groups

Subgroups A and B of a finite group are said to be totally permutable if every subgroup of A permutes with every subgroup of B. The behaviour of finite pairwise totally permutable products are studied with respect to certain classes of groups including the class of groups where all the subnormal subgroups permute with all the maximal subgroups, the so-called SM-groups, and also the class of groups where all the subnormal subgroups are permutable, the so-called PT-groups.