| 超幂零群的性质研究 |
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| 引用本文： | 张佳,郭继东. 超幂零群的性质研究[J]. 江汉大学学报(自然科学版), 2013, 41(1): 23-26 |
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| 作者姓名： | 张佳 郭继东 |
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| 作者单位： | 伊犁师范学院 数学与统计学院,新疆伊宁,835000 |
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| 基金项目： | 国家自然科学基金资助项目,新疆自然科学基金,新疆伊犁师范学院2012年度大学生课题 |
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| 摘 要： | 幂零群的研究一直是有限群理论研究的重要组成部分。我们知道幂零群G存在正规群列:G=G1Gr=1,因子群GiGi+1￡Z(G Gi+1)。本文研究幂零群的推广。假设群的因子群是超中心的及GiGi+1是循环群,在此基础上,引出超幂零群的概念。利用有限群理论对有限超幂零群的性质进行研究,得到一些有意义的结果。
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| 关 键 词： | 超中心 群列 超幂零群 特征子群 |
Research of Properties of Super Nilpotent Group |
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| ZHANG Jia , GUO Ji-dong. Research of Properties of Super Nilpotent Group[J]. Journal of Jianghan University(Natural Sciences), 2013, 41(1): 23-26 |
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| Authors: | ZHANG Jia GUO Ji-dong |
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| Affiliation: | (College of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China) |
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| Abstract: | The research of nilpotent groups is a important part of the research of finite groups' theory.The research report of nilpotent groups is plentiful.Decribing properties of nilpotent groups is also difficult.As known,nilpotent groups G have a normal subgroups series:G = G1…Gr = 1 which makes Gi Gi + 1￡ Z(G Gi + 1)(i=1,2,…,r) discusses the generalization of nilpotent groups.Assumes that the factor group is super central and Gi Gi + 1 is cyclic group.According to it,intro duces a definition of super nilpotent groups.Discuss super nilpotent groups' properties with using the theory of finite groups,obtains some meaningful conclusions. |
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| Keywords: | super center group series super nilpotent group characterization subgroup |
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