A criterion of p-nilpotency of finite groups with some weakly s-semipermutable subgroups

Abstract

Let H be a subgroup of a group G.  H is called a weakly s-semipermutable subgroup of G if there are a subnormal subgroup T of G and an s-semipermutable subgroup H_ssG in G contained in H such that G = HT and H ∩ T ≤ H_ssG.  In this paper, we got a criterion of p-nilpotency of G by some weakly s-semipermutable subgroups.