Structure of augmentation quotients of finite homocyclic abelian groups

被引：4
|
作者：
Tang, Guo-ping [1 ]
机构：
[1] Chinese Acad Sci, Grad Univ, Sch Math, Beijing 100049, Peoples R China
来源：
SCIENCE IN CHINA SERIES A-MATHEMATICS | 2007年 / 50卷 / 09期
基金：
中国国家自然科学基金;
关键词：
integral group ring; augmentation ideal; consecutive quotient of augmentation ideal;
D O I：
10.1007/s11425-007-0112-6
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Let G be a finite abelian group and its Sylow p-subgroup a direct product of copies of a cyclic group of order p(r), i.e., a finite homocyclic abelian group. Let Delta(n) (G) denote the n-th power of the augmentation ideal A(G) of the integral group ring ZG. The paper gives an explicit structure of the consecutive quotient group Q(n)(G) = Delta(n)(G)/Delta(n+1)(G) for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.
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页码：1280 / 1288
页数：9
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