Weakly s-supplemented subgroups and p-nilpotency of finite groups

A subgroup H of a group G is said to be weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ H _sG , where H _sG is the maximal s-permutable subgroup of G contained in H. In this paper, we investigate the influence of weakly s-supplemented subgroups on the structure of finite groups. Some recent results are generalized.