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| S-拟正规子群对有限群结构的影响 |
| Influence of S-quasinormal Subgroups on the Structure of Finite Groups |
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| DOI：10.3969/j.issn.1671-5322.2005.03.003 |
| 中文关键词: S-拟正规 p-幂零 p-超可解 |
| 英文关键词: S-quasinormal p-nilpotent p-supersoluble |
| 基金项目: |
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| 摘要点击次数: 3415 |
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| 中文摘要: |
| 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. |
| 英文摘要: |
| 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. |
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