| 几类非Abel群之增广商群的结构 |
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| 引用本文： | 赵红梅,唐国平.几类非Abel群之增广商群的结构[J].数学进展,2008,37(2):163-170. |
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| 作者姓名： | 赵红梅 唐国平 |
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| 作者单位： | 1. 西北工业大学理学院,西安,陕西,710072
2. 中国科学院研究生院数学系,北京,100049 |
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| 摘 要： | 记ZG为有限群G的整群环,△n(G)为增广理想△(G)的n次幂,Qn(G)=△"(G)/△n 1(G)为G的增广商群.本文考虑了二面体群D2tk(k 奇)和m次对称群Sm,证明了Qn(D2tk)为秩不超过2t 1的基本2-群以及Qn(Sm)≌Z2.
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| 关 键 词： | 整群环 增广商群 二面体群 对称群 integral group ring augmentation quotient group dihedral group symmetric group Abel 群的结构 Groups Augmentation Quotient elementary rank show symmetric group paper augmentation quotient groups power augmentation ideal integral group ring finite group 对称群 二面体群 增广商群 增广理想 整群环 |
| 文章编号： | 1000-0917(2008)02-0163-08 |
| 修稿时间： | 2006年3月15日 |
On the Structure of the Augmentation Quotient Groups for Some Nonabelian Groups |
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| ZHAO Hongmei,TANG Guoping.On the Structure of the Augmentation Quotient Groups for Some Nonabelian Groups[J].Advances in Mathematics,2008,37(2):163-170. |
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| Authors: | ZHAO Hongmei TANG Guoping |
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| Abstract: | Let G be a finite group,ZG its integral group ring and △n(G)the nth power of the augmentation ideal △(G),denote Qn(G)=△n(G)/△n+1(G)the augmentation quotient groups of G.In this paper,dihedral group D2tk(k odd)and m'th symmetric group Sm are considered.We show Qn(D2tk)is an elementary 2-group and its rank is no more than 2t+1.As for Qn(Sm),we have Qn(Sm)≌Z2. |
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| Keywords: | integral group ring augmentation quotient group dihedral group symmetric group |
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