On finite groups with s-weakly normal subgroups

A subgroup H of a group G is weakly normal in G if H-g <= N-G(H) implies that g is an element of N-G(H) for any element g is an element of G. A subgroup H of a group G is s-weakly normal in G if there exists a normal subgroup T such that G = HT and H boolean AND T is weakly normal in G. Clearly a weakly normal subgroup of G is an s-weakly normal subgroup of G. In this paper, we investigate the influence of s-weakly normal subgroups on the structure of a finite group, especially some criteria for supersolvability, nilpotency, formation and hypercenter of a finite group are proved. Based on our results, some recent results can be generalized easily.