On weakly s-permutable subgroups of finite groups

A subgroup H of a group G is said to be weakly s-permutable in G if there exists a subnormal subgroup K of G such that G = HK and H ∩ K ≤ H _sG where H _sG is the largest s-quasinormal subgroup of G contained in H. In this paper, we investigate the influence of weak s-permutability of some primary subgroups in finite groups. Some new results about p-supersolvability and p-nilpotency of finite groups are obtained.