交换p群的整群环以及它的极大序的K1群  

The K1 group of integral group ring and its maximal order for a commutative p group

作　　者：杨全李 唐国平 YANG Quanli;TANG Guoping(School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院大学数学科学学院,北京100049

出　　处：《中国科学院大学学报（中英文）》2020年第5期577-581,共5页Journal of University of Chinese Academy of Sciences

基　　金：国家自然科学基金(11771422)资助。

摘　　要：整群环是代数乃至许多数学分支中很重要的一类环,也是代数K理论主要的研究对象之一。对几类交换p(p为素数)群G的整群环ZG,作为半单代数QG的一个Z-序,通过将其嵌入到极大Z-序Γ之中,然后利用核群的性质研究K 1(ZG)在K1(Γ)中的指数问题。主要结果有:首先对几类交换p群G给出[(Γp)×∶(ZpG)×]的确切表达式,然后用来确定[K1(Γ)∶K1(ZG)]的具体数值。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-orderΓ.Then we use the properties of the kernel group to study the exponential problem of K 1(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.

关 键 词：整群环 Z-序 极大序 核群 K 1群 

分 类 号：O154.3[理学—数学]