| 关于有限群的共轭置换子群 |
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| 引用本文： | 张新建.关于有限群的共轭置换子群[J].淮阴师范学院学报(自然科学版),2009,8(3):173-176. |
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| 作者姓名： | 张新建 |
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| 作者单位： | 淮阴师范学院,数学系,江苏,淮安,223300;苏州大学,数学科学学院,江苏,苏州,215006 |
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| 基金项目： | 国家自然科学基金项目，江苏省自然科学资助项目 |
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| 摘 要： | 群G的子群H称为在G中共轭置换,若HgH=HHg对任意的g∈G成立.本文利用共轭置换子群的概念研究了群的幂零性和超可解性的问题,获得了一个群为幂零群或超可解群的几个等价条件和充分条件.
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| 关 键 词： | 共轭置换子群 极小非幂零群 幂零群 超可解群 |
On the Conjugate-permutable Subgroups of Finite Groups |
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| ZHANG Xin-jian.On the Conjugate-permutable Subgroups of Finite Groups[J].Journal of Huaiyin Teachers College(Natrual Science Edition),2009,8(3):173-176. |
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| Authors: | ZHANG Xin-jian |
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| Institution: | ZHANG Xin-jian(1.Department of mathematics,Huaiyin Teachers College,Huaian Jiangsu 223300,China)(2.School of Mathematical Science,Soochow University,Suzhou Jiangsu 215006,China) |
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| Abstract: | A subgroup H of a group G is called conjugate-permutable in G if it is permutable with every conjugate subgroups Hg of H for all g∈G.In this paper,the influences of conjugate permutability on nilpotency and supersolvability of finite groups are investigated.Some equivalent and sufficient conditions for a group to be nilpotent and supersolvable are obtained. |
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| Keywords: | conjugate-permutable subgroup minimal non-nilpotent group nilpotent group supersolvable group |
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