| 典型群的增广商群 |
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| 引用本文： | 赵辉芳,南基洙.典型群的增广商群[J].中国科学:数学,2012,42(12):1225-1235. |
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| 作者姓名： | 赵辉芳 南基洙 |
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| 作者单位： | 南昌航空大学数学与信息科学学院, 南昌 330063;
大连理工大学数学科学学院, 大连 116024 |
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| 基金项目： | 国家自然科学基金(批准号: 10771023) 资助项目 |
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| 摘 要： | 设G 为有限域K 上的一般线性群(特殊线性群、酉群、辛群及正交群), 记整群环ZG 的n 次增广理想为△n(G). 本文着重研究有限域上的典型群的增广商群Qn(G) = △n(G)/△n+1(G), 并刻画了这些连续商群的结构.
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| 关 键 词： | 整群环 增广理想 增广商群 典型群 |
Augmentation quotients of some classical groups |
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| ZHAO HuiFang,NAN JiZhu.Augmentation quotients of some classical groups[J].Scientia Sinica Mathemation,2012,42(12):1225-1235. |
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| Authors: | ZHAO HuiFang NAN JiZhu |
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| Abstract: | Let K be a finite field, and let G be the general linear group (the special linear group, the unitary group, the symplectic group and the orthogonal group, etc.) over K, ZG its integral group ring and △(G) its n-th augmentation ideal. In this paper, we study the consecutive quotients Qn(G) = △n(G)=△n+1(G) of the classical group over finite fields and therefore completely determine the structure of such consecutive quotient groups. Keywords integral group ring, augmentation ideal, augmentation quotient group, classical groups |
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| Keywords: | integral group ring augmentation ideal augmentation quotient group classical groups |
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