循环群的极大子群作用下的Burnside环的连续商群

Consecutive quotients of powers of Burnside ring of a cyclic group under action by the maximal subgroup

研究有限循环群的任一极大子群作用下的Burnside环的增广理想的基底,给出n次增广理想的一般表达式,并进一步讨论其连续商群的结构问题,得到一般情形下的同构分解式.

In this work, the basis of augmentation ideal I of Burnside ring of a finite cyclic group under the action by any maximal subgroup is studied. The reeursion formula of the nth power In of the augmentation ideal I is given. Furthermore, the consecutive quotient In/I^（n＋1） of the nth power In by the （n ＋ 1 ） th power of the ideal I is discussed, and its structure is determined in general.