Structure of augmentation quotients of finite homocyclic abelian groups

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 pr,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.