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Influence of S-quasinormal Subgroups on the Structure of Finite Groups

If there exists a subgroup A of G such that AG_p=G_pA and p||G|,then A is a S- quasinormality subgroup of G. Let G be a finite group.In this paper, we study the structure of finite group G by using of the quasinormality of subgroups, condition and obtain some sufficient conditions for a group belonging to p-nilpotent groups and p-superslovable groups. Particularly, the author proves the following result:Let G be a group,N/G,and N be p- soluble, G/N be p- supersoluble. If every maximal subgroup of Sylow p- subgroup is S- quasinormalied in G, then G is p-superslovable. Moreover,some relevant results are generalized.