| Structure of augmentation quotients of finite homocyclic abelian groups |
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| 作者姓名： | Guo-ping TANG School of Mathematical Sciences Graduate University of Chinese Academy of Sciences Beijing China |
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| 作者单位： | Guo-ping TANG School of Mathematical Sciences，Graduate University of Chinese Academy of Sciences，Beijing 100049，China |
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| 基金项目： | 国家自然科学基金;中国科学院"百人计划" |
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| 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.LetΔ~n (G) denote the n-th power of the augmentation idealΔ(G) of the integral group ring ZG.The paper gives an explicit structure of the consecutive quotient group Q_n(G)=Δ~n(G)/Δ~(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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Structure of augmentation quotients of finite homocyclic abelian groups |
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| Guo-ping TANG School of Mathematical Sciences,Graduate University of Chinese Academy of Sciences,Beijing ,China.Structure of augmentation quotients of finite homocyclic abelian groups[J].Science in China(Mathematics),2007,50(9):1280-1288. |
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| Authors: | Guo-ping Tang |
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| Institution: | School of Mathematical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China |
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| Abstract: | 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 Δ
n
(G) denote the n-th power of the augmentation ideal Δ(G) of the integral group ring ℤG. The paper gives an explicit structure of the consecutive quotient group Q
n
(G) = Δ
n
(G)/Δ
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.
This work was supported by the National Natural Science Foundation of China (Grant No. 10271094) and “Hundred Talent” Program
of the Chinese Academy of Sciences |
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| Keywords: | integral group ring augmentation ideal consecutive quotient of augmentation ideal |
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