Group rings are very important rings in algebra and many other branches of mathematics. It is also one of the main research subjects of algebraic K-theory. In this work, we mainly deal with integral group rings ZG for some abelian p(p is prime) groups G. We can regard ZG as a Z-order of the semi-simple algebra QG and embed it into the maximal Z-order Γ. Then we use the properties of the kernel group to study the exponential problem of K1(ZG) in K1(Γ). In this paper, there are two main results. First, the explicit formula of[(Γp)×:(ZpG)×] is obtained for some abelian p groups. Secondly,by using the formula,we get the specific result of[K1(Γ):K1(ZG)] for some abelian p groups.
YANG Quanli
,
TANG Guoping
. The K1 group of integral group ring and its maximal order for a commutative p group[J]. Journal of University of Chinese Academy of Sciences, 2020
, 37(5)
: 577
-581
.
DOI: 10.7523/j.issn.2095-6134.2020.05.001
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