| 一类整群环的K1群的计算 |
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| 引用本文： | 刘佳奇,高玉彬. 一类整群环的K1群的计算[J]. 中国科学院大学学报, 2011, 28(2): 141-146. DOI: 10.7523/j.issn.2095-6134.2011.2.002 |
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| 作者姓名： | 刘佳奇 高玉彬 |
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| 作者单位： | 1. 中国科学院研究生院数学科学学院, 北京 100049;2. 北京航空航天大学数学与系统科学学院, 北京 100191 |
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| 基金项目： | 国家自然科学基金(10671202)和中国科学院百人计划项目资助 |
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| 摘 要： | 着重讨论整群环的 K1群的计算,问题的关键点在于其对应的SK1群的计算,其中,p群的整群环的SK1群的结果是已知的.讨论了计算SK1群的基本理论,并证明了一类特殊的非p群(p-1q-1阶群)的整群环的SK1 群是平凡的.
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| 关 键 词： | 整群环 ZG K1群 SK1群 p群 非p群 |
| 收稿时间： | 2010-04-27 |
| 修稿时间： | 2010-05-20 |
Calculation of K1 group of some integral group rings |
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| LIU Jia-Qi,GAO Yu-Bin. Calculation of K1 group of some integral group rings[J]. , 2011, 28(2): 141-146. DOI: 10.7523/j.issn.2095-6134.2011.2.002 |
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| Authors: | LIU Jia-Qi GAO Yu-Bin |
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| Affiliation: | 1. School of Mathematical Sciences, Chinese Academy of Sciences, Beijing 100049, China;2. School of Mathematics and System Science, Beijing University of Aeronautics & Astronautics, Beijing 100191, China |
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| Abstract: | The integral group ring ZG is an important ring structure. This paper focuses on the calculation of the K1 groups of integral group rings. The key point of the problem lies in the calculation of their corresponding SK1 group rings. The SK1 groups of the integral group rings of p groups are relatively easy to calculate,but the SK1 groups of the integral group rings of non-p groups are relatively diffcult to calculate. This article discusses the basic theory of the problem.Furthermore,this article also treats the groups whose orders are p1q1 and discusses the calculation of the SK1 group rings of their integral group rings. |
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| Keywords: | integral group ring ZG K1 group SK1 group p group non-p group |
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