摘要
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NG,且N为p-可解群,G/N为p-超可解群。若N的每个Sylowp-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。
If there exists a subgroup A of G such that AGp = GpA 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.
出处
《盐城工学院学报（自然科学版）》
CAS
2005年第3期9-12,共4页
Journal of Yancheng Institute of Technology:Natural Science Edition
