Structure of augmentation quotients of finite homocyclic abelian groups  

作　　者：Guo-ping TANG School of Mathematical Sciences,Graduate University of Chinese Academy of Sciences,Beijing 100049,China 

出　　处：《Science China Mathematics》2007年第9期1280-1288,共9页中国科学：数学（英文版）

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

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 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.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.LetΔⁿ （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）=Δⁿ（G）/Δⁿ⁺¹（G） for any natural number n and as a consequence settles a problem of Karpilovsky for this particular class of finite abelian groups.

关 键 词：integral group ring augmentation ideal consecutive quotient of augmentation ideal 16S34 20C05 

分 类 号：O152[理学—数学]