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.