Finite groups with some m-permutable primary subgroups

Let d be the smallest generator number of a finite p-group P and Md (P) = {P1,P2,...
Pd} be the set of maximal subgroups of P such that ?d,i =1 Pi = ?(P). Then P is called M-permutable in a finite group G, if there exists a subgroup B of G such that G = PB and PiB < G for every Pi of Md (P). In this paper, we investigate the structure of finite groups by some M-permutable subgroups of the Sylow p-subgroup. Some new results about p-supersolvable groups and p-nilpotent groups are obtained.