整群环的增广理想之幂的基底及其商群的结构

Basis of powers of the augmentation ideal of integer group ring and the structure of their quotient groups

目的 计算特殊整群环的增广理想之幂的基底及确定其商群的结构。方法 通过增广理想中的关系,从生成元中找出基底元。结果 得到了该整群环的增广理想之幂的基底,进而确定了其商群的结构。结论 回答了关于此类特殊群的Karpilovsky问题。

Aim The basis for powers of the augmentation ideal of one kind of special abelian groups is computed. Then the structure of their consecutive quotient groups is determined. Methods The basis elements can be found among the generated elements by the relations of powers of the augmentation ideal.Results A basis for the powers of the augmentation ideal is found and the structure of quotient groups is established.Conclusion The results answered an open problem of Karpilovsky for this special kind of groups.