The influence of S-embedded subgroups on the structure of finite groups

Let H be a subgroup of a group G. H is said to be S-embedded in G if G has a normal T such that HT is an S-permutable subgroup of G and H ∩ T ≤ H sG, where H denotes the subgroup generated by all those subgroups of H which are S-permutable in G. In this paper, we investigate the influence of minimal S-embedded subgroups on the structure of finite groups. We determine the structure the finite groups with some minimal S-embedded subgroups. We also give some new characterizations of p-nilpotency of finite groups in terms of S-embedding property. As applications, some previous known results are generalized.