S-quasinormallity of finite groups

Let d be the smallest generator number of a finite p-group P, and let ℳ _d (P) = {P ₁,..., P _d } be a set of maximal subgroups of P such that ∩ _i=1 ^d P _i =Φ(P). In this paper, the structure of a finite group G under some assumptions on the S-quasinormally embedded or SS-quasinormal subgroups in ℳ _d (P), for each prime p, and Sylow p-subgroups P of G is studied.