The S-Quasinormal Embedding Property of Subgroups in a Finite Group

A subgroup H of a finite group G is called S-quasinormally embedded in G if a Sylow subgroup of H is also a Sylow subgroup of some S-quasinormal subgroup of G. In this paper, the structure of a finite group G with some S-quasinormally embedded subgroups of Sylow p-subgroups with a fixed order is characterized and some known related results on p-nil potency of finite groups are generalized.