The influence of S-quasinormality of some subgroups of prime power order on the structure of finite groups

Let G be a finite group. Two subgroups H and K of G are said to permute if [H, K] = HK = KH. A subgroup H of G is S-quasinormal in G if it permutes with every Sylow subgroup of G. In this paper we investigate the influence of S-quasinormality of some subgroups of prime power order of a finite group on its supersolvability.