| U(4,Z)的自同构群(英文) |
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| 引用本文： | 王玉雷,孙大为,王志俊.U(4,Z)的自同构群(英文)[J].数学季刊,2012(1):98-103. |
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| 作者姓名： | 王玉雷 孙大为 王志俊 |
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| 作者单位： | Department of Mathematics,Henan University of Technology;Department of Mathematics,China University of Mining and Technology |
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| 基金项目： | Supported by the Tianyuan Fund for Mathematics of NSFC(11126273);Supported by the NSF of Henan Educational Committee(2011B110011);Supported by the Doctor Foundation of Henan University of Technology(2009BS029) |
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| 摘 要： | In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then （i） InnG ■ K ■ AutG;（ii） AutG/K≌=G1×D8×Z2,where G1=(a,b,c|a4=b2=c2=1,ab=a-1,a,c]= b,c]=1 ;（iii） K/Inn G≌=Z×Z×Z.
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| 关 键 词： | upper unitriangular matrix groups general linear groups automorphism groups |
The Automorphism Group of U(4,Z) |
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| WANG Yu-lei,SUN Da-wei,WANG Zhi-jun.The Automorphism Group of U(4,Z)[J].Chinese Quarterly Journal of Mathematics,2012(1):98-103. |
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| Authors: | WANG Yu-lei SUN Da-wei WANG Zhi-jun |
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| Institution: | 1.Department of Mathematics,Henan University of Technology,Zhengzhou 450001,China;2.Department of Mathematics,China University of Mining and Technology,Xuzhou 221116,China) |
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| Abstract: | In this paper,the automorphism group of G is determined,where G is a 4 × 4 upper unitriangular matrix group over Z.Let K be the subgroup of AutG consisting of all elements of AutG which act trivially on G/G,G /ζG and ζG,then （i） InnG ■ K ■ AutG;（ii） AutG/K≌=G1×D8×Z2,where G1=(a,b,c|a4=b2=c2=1,ab=a-1,a,c]= b,c]=1 ;（iii） K/Inn G≌=Z×Z×Z. |
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| Keywords: | upper unitriangular matrix groups general linear groups automorphism groups |
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