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 ‎H\cap T\leq 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 G‎. ‎Some new results were obtained.‎

Keywords:

s-permutable subgroup , SS-embedded subgroup , p-nilpotent group , Sylow tower group