S-quasinormallity of finite groups

Abstract

Let d be the smallest generator number of a finite p-group P, and let ℳd(P) = {P1,..., Pd} be a set of maximal subgroups of P such that ∩i=1dPi=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 ℳd(P), for each prime p, and Sylow p-subgroups P of G is studied.