| 表特殊线性群中元素为平延换位子之积 |
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| 引用本文： | 游宏,郑宝东.表特殊线性群中元素为平延换位子之积[J].数学进展,2001,30(2):133-140. |
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| 作者姓名： | 游宏 郑宝东 |
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| 作者单位： | 哈尔滨工业大学数学系, |
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| 基金项目： | The project supported by
NSFC (No.19871018) and project (HIT.2000.02) supported by the Scientific Research
Foundation of Harbin Institute of Technology. |
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| 摘 要： | 考虑元素了数大于3的域F上的特殊线性群SLnF.对GLnF中任一矩阵A，记resA为A－I的秩，称矩阵A为平延，如果resA=I并且 detA=1,对n≥2，本文证明SLnF中任一矩阵都可写成不超过resA/2] 2个平延换位子之积。
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| 关 键 词： | 特殊经性群 平延 换位子 域 矩阵 |
| 修稿时间： | 1998年6月19日 |
The Elements of the
Special Linear Group SLnF as Products of Commutators of Transvections |
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| You Hong,Zheng Baodong.The Elements of the
Special Linear Group SLnF as Products of Commutators of Transvections[J].Advances in Mathematics,2001,30(2):133-140. |
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| Authors: | You Hong Zheng Baodong |
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| Abstract: | We consider the special linear group SLnF over a field F with more than three elements.Let resA denote rank(A-I) for any A in GLnF.A matrix A is called a transvection if resA＝1 and detA＝1. For n＞2,we prove that every matrix A in SLn F is a productof at most resA/2]+2 Commutators of transvections. |
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| Keywords: | special linear group transvection commutator field |
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