一类整群环的K_1群的计算

Calculation of K_1 group of some integral group rings

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(p1q1阶群)的整群环的SK1群是平凡的.

The integral group ring G 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.