Abstract: A subgroup H of group G is said to be weakly S-semipermutabe in G if there exists a subnormal subgroup B of G such that G=HB and H∩B≤H_ssG,where H_ssG is the maximal S-semipermutable subgroup of G contained in H.By using the weakly S-semipermutability of the maximal subgroups of the Sylow subgroup and combining the normalizer  of Sylow subgroup,a sufficient condition for a finite group to be p-nilpotent is obtained and some recent results can be generalized.

Key words: S-permutable, S-permutably embedded, weakly S-semipermutable, p-nilpotent