| 超幂零群的性质研究 |
| |
| 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. |
| |
| 作者姓名： | 张佳 郭继东 |
| |
| 作者单位： | 伊犁师范学院 数学与统计学院,新疆伊宁,835000 |
| |
| 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 |
| |
| 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。
|
| 关 键 词： | 超中心 群列 超幂零群 特征子群 |
Research of Properties of Super Nilpotent Group |
| |
| ZHANG Jia
,
GUO Ji-dong.Research of Properties of Super Nilpotent Group[J].Journal of Jianghan University:Natural Sciences,2013,41(1):23-26. |
| |
| Authors: | ZHANG Jia GUO Ji-dong |
| |
| Institution: | (College of Mathematics and Statistics,Yili Normal University,Yining 835000,Xinjiang,China) |
| |
| 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. |
| |
| Keywords: | super center group series super nilpotent group characterization subgroup |
| 本文献已被 CNKI 万方数据 等数据库收录！ |
|
