| 有限群的超可解与幂零性质(英文) |
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| 引用本文： | 赵,涛.有限群的超可解与幂零性质(英文)[J].苏州科技学院学报(自然科学版),2014(2):6-12. |
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| 作者姓名： | 赵 涛 |
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| 作者单位： | 山东理工大学理学院,山东淄博255049 |
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| 基金项目： | 国家自然科学基金资助项目（11171243） |
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| 摘 要： | 设H是有限群G的一个子群,若存在子群B使得HB=G且H与B的每个Sylow都可换,则称H在G中SS-拟正规。如果存在G的正规子群T使得HT在G中s-可换,H∩T在G中SS-拟正规,则称H为G的弱SS-拟正规子群。文中研究了某些弱SS-拟正规子群对有限群结构的影响。一系列原有的结论得到了统一和推广。
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| 关 键 词： | SS-拟正规子群 弱SS-拟正规子群 p-幂零群 超可解群 |
Supersolubility and nilpotency of finite groups |
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| ZHAO Tao.Supersolubility and nilpotency of finite groups[J].Journal of University of Science and Technology of Suzhou,2014(2):6-12. |
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| Authors: | ZHAO Tao |
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| Institution: | ZHAO Tao (School of Science, Shandong University of Technology, Zibo 255049, China) |
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| Abstract: | Suppose that H is a subgroup of a finite group G and that there exists a subgroup B. If HB=G and H is per-mutable with every Sylow subgroup of B,H is SS-quasinormal in G. Suppose that there exists a normal subgroup T of G and that HT is s-permutable. If H∩T is SS-quasinormal in G,H is a weakly SS-quasinormal subgroup of G. In this pa-per, we have investigated the influence of some weakly SS-quasinormal subgroups on the structure of finite groups. A se-ries of known results in the literature are unified and generalized. |
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| Keywords: | SS-quasinormal subgroup weakly SS-quasinormal subgroup p-nilpotent group supersolvable group |
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