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.

Key words: integral group ring ZG, K₁ group, SK₁ group, p group, non-p group