Z-permutable subgroups of finite groups

Let ℨ be a complete set of Sylow subgroups of a finite group G, that is, a set composed of a Sylow p-subgroup of G for each p dividing the order of G. A subgroup H of G is called ℨ-permutable if H permutes with all members of ℨ. The main goal of this paper is to study the embedding of the ℨ-permutable subgroups and the influence of ℨ-permutability on the group structure