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<sup>r</sup>,i.e.,a finite homocyclic abelian group.LetΔ<sup>n</sup> （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<sub>n</sub>（G）=Δ<sup>n</sup>（G）/Δ<sup>n+1</sup>（G） for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.
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 ?G. 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.
基金
This work was supported by the National Natural Science Foundation of China (Grant No.10271094)
"Hundred Talent"Program of the Chinese Academy of Sciences
