中文摘要：

Let P be a Sylow p-subgroup of a group G with the smallest generator number d,where p is a prime.Denote by Md（P） = {P1,P2,...,Pd} a set of maximal subgroups of P such that φ（P） = ∩n=1dPn.In this paper,we investigate the structure of a finite group G under the assumption that the maximal subgroups in Md（P） are weakly s-permutably embedded in G,some interesting results are obtained which generalize some recent results.Finally,we give some further results in terms of weakly s-permutably embedded subgroups.

英文摘要：

Let P be a Sylow p-subgroup of a group G with the smallest generator number d, where p is a prime. Denote by Md（P） = （P1, P2,..., Pd） a set of maximal subgroups of P such that φ（P） = ∩n^d=1Pn. In this paper, we investigate the structure of a finite group G under the assumption that the maximal subgroups in Md（P） are weakly s-permutably embedded in G, some interesting results are obtained which generalize some recent results. Finally, we give some further results in terms of weakly s-permutably embedded subgroups.