p-群的Burnside环的增广理想的商群的结构

The structure of powers of the augmentation ideal and their consecutive quotients for the Burnside ring of p-Group

目的讨论两类由p-群出发构造的Burnside环的增广理想的商群的结构。方法利用轨道、稳定子和基底的关系,归纳证明。结果确定了该商群的结构。结论回答了关于此类Burnside环的Karpilovsky问题。

Aim To discuss the consecutive quotients of powers of the augmentation ideal for the Burnside ring of p-group discussed. Methods The results can be obtained and proved by using the relation among the orbit, the stabilizer. Results The structure for such quotients is established for such p-group. Conclusion The results answered an open problem of Karpilovsky for this kind of Burnside ring.