s-conditionally Permutable Subgroup and the Supersoluble Property of Finite Group

A subgroup H of a finite group G is s-conditionally permutable in G if for every Sylow subgroup P of G there is an element z∈G such that HPz=PzH.In this paper,some subgroups with prime power order by its s-conditionally permutable properties were studied and some sufficient conditions were obtained about supersoluble group.