S-拟正规子群对有限群结构的影响

如果群G的子群A与G的每个Sylow子群Gp可交换（即AGp=GpA），则称A为G的S-拟正规子群。对任意有限群G，我们利用子群的S-拟正规性刻划群G的结构，给出G为p-幂零群和p-超可解群的若干充分条件，特别证明了如下结果：设N△G，且N为p-可解群，G／N为p-超可解群。若N的每个Sylow p-子群（或循环p-子群）的极大子群在G内S-拟正规，则G为p-超可解群，并推广了相关文献的结果。

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.