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中国科学院大学学报 ›› 2013, Vol. 30 ›› Issue (3): 289-292.DOI: 10.7523/j.issn.1002-1175.2013.03.001

• 数学 •    下一篇

整群环上核群D(ZG)的一个注记

刘佳, 唐国平   

  1. 中国科学院研究生院数学科学学院, 北京 100049
  • 收稿日期:2012-03-28 修回日期:2012-05-15 发布日期:2013-05-15
  • 通讯作者: 刘佳,liujia0509@mails.ucas.ac.cn
  • 基金资助:

    国家自然科学基金(11071247)资助 

A note on the kernel group of an integral group ring

LIU Jia, TANG Guo-Ping   

  1. School of Mathematical Sciences, Graduate University, Chinese Academy of Sciences, Beijing 100049, China
  • Received:2012-03-28 Revised:2012-05-15 Published:2013-05-15

摘要:

G为一有限群, Λ为群代数QG的一个Z-序, Λ'为包含Λ的一个极大Z-序. 由包含映射诱导出的局部自由类群CL(Λ)CL(Λ')的同态映射的核定义为核群D(Λ). 当G为有限p-群时, 对D(ZG)的指数给出一个估计.

关键词: 整群环, 核群D(ZG), 极大Z-序

Abstract:

Let G be a finite group, Λ be a Z-order of group algebra QG, and Λ' be a maximal Z-order containing Λ. There is a homomorphism between locally free groups CL(Λ) and CL(Λ') which is induced by including map, and the kernel group D(Λ) is defined to be the kernel of this homomorphism. When G is a p-group, we give an estimate of the exponent of the kernel group D(ZG).

Key words: integral group ring, kernel group D(ZG), maximal Z-order

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