收稿日期: 2010-04-27
修回日期: 2010-05-20
网络出版日期: 2011-03-15
基金资助
国家自然科学基金(10671202)和中国科学院百人计划项目资助
Calculation of K1 group of some integral group rings
Received date: 2010-04-27
Revised date: 2010-05-20
Online published: 2011-03-15
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
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.
Key words： integral group ring ZG; K1 group; SK1 group; p group; non-p group
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