On M-permutable maximal subgroups of sylow subgroups of finite groups

摘要

Let d be the smallest generator number of a finite p-group P, and let M_d(P) = {P_1, P_2, . .., P_d} be a set of maximal subgroups of P such that ~∩_(i=1)~d P_i = Φ(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 P_iB < G for any P_i of M_d(P). In this article, we investigate the influence of M-permutability of some primary subgroups in finite groups. Some new results about supersolvable groups and formations are obtained.