Some Characterizations of p-Nilpotency for Finite Groups

Let A be a subgroup of group G,and X a non-empty subset of G.A is said to be X-s-semipermutable in G if A has a supplement T in G such that A is X-permutable with every Sylow subgroup of T.In this paper,the influences of X-s-semipermutability of some subgroups on the structure of finite groups are investigated.Some new criteria for group G to be p-nilpotent are obtained.