Finite groups with some SS-embedded subgroups

We call H an SS-embedded subgroup of G if there exists a normal subgroup T of G such that HT is subnormal in G and Hcap Tleq H_{sG}, where H_{sG} is the maximal s-permutable subgroup of G contained in H. In this paper, we investigate the influence of some SS-embedded subgroups on the structure of a finite group. Some new results were obtained.