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中国科学院大学学报 ›› 2016, Vol. 33 ›› Issue (3): 302-305.DOI: 10.7523/j.issn.2095-6134.2016.03.003

• 数学与物理学 • 上一篇    下一篇

循环群的极大子群作用下的Burnside环的连续商群

武海波1, 唐国平2   

  1. 1. 西北工业大学理学院, 西安 710072;
    2. 中国科学院大学数学科学学院, 北京 100049
  • 收稿日期:2015-04-13 修回日期:2015-10-09 发布日期:2016-05-15
  • 通讯作者: 唐国平
  • 基金资助:

    国家自然科学基金(11371343)和西北工业大学基础研究基金(JCY20130139)资助

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

WU Haibo1, TANG Guoping2   

  1. 1. School of Science, Northwestern Polytechnical University, Xi'an 710072, China;
    2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China
  • Received:2015-04-13 Revised:2015-10-09 Published:2016-05-15

摘要:

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.

关键词: Burnside环, 增广理想, 连续商群

Abstract:

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 recursion 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.

Key words: Burnside ring, augmentation ideal, consecutive quotient

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