Denote by Dm the dihedral group of order 2m. Let R（Dm） be its complex representation ring, and let △（Dm） be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quoti...Denote by Dm the dihedral group of order 2m. Let R（Dm） be its complex representation ring, and let △（Dm） be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient △^n（Dm）/△^n＋1（Dm） for each positive integer n.展开更多
Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n...Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.展开更多
In this article we describe the stable behavior of the augmentation quotients Qn （G） for the groups G of order p^5 with even numbers of generators, where p is an odd prime.
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...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?G.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.展开更多
文摘Denote by Dm the dihedral group of order 2m. Let R（Dm） be its complex representation ring, and let △（Dm） be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient △^n（Dm）/△^n＋1（Dm） for each positive integer n.
基金supported by the National Natural Science Foundation of China(Nos.11226066,11401155)Anhui Provincial Natural Science Foundation(No.1308085QA01)
文摘Abstract Denote by Qm the generalized quaternion group of order 4m. Let R（Qm） be its complex representation ring, and △（Qm） its augmentation ideal. In this paper, the author gives an explicit Z-basis for the △n（Qm） mid determines the isomorphism class of the n-th augmentation quotient for each positive integer n.
文摘In this article we describe the stable behavior of the augmentation quotients Qn （G） for the groups G of order p^5 with even numbers of generators, where p is an odd prime.
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
文摘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?G.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.
