Structure of augmentation quotients of finite homocyclic abelian groups
Structure of augmentation quotients of finite homocyclic abelian groups
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DOI：
10.1007/s11425-007-0112-6
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发表时间：
2007-09
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影响因子：
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通讯作者：
G. Tang
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文献类型：
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作者：
G. Tang
假设一个有限阿贝尔群及其sylop -子群是一个有序环群的拷贝的直积，即一个有限齐环阿贝尔群。设Δn(G)表示整数群环的增广理想Δ(G)的次幂。本文给出了任意自然数的连续商群qn (G) = Δn(G)/Δn+1(G)的一个显式结构，从而解决了该类有限阿贝群的Karpilovsky问题。
LetGbe a finite abelian group and its Sylowp-subgroup a direct product of copies of a cyclic group of orderpr, i.e., a finite homocyclic abelian group. Let Δn(G) denote then-th power of the augmentation ideal Δ(G) of the integral group ring ℤG. The paper gives an explicit structure of the consecutive quotient groupQn(G) = Δn(G)/Δn+1(G) for any natural numbernand as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.