U(4,Z)的自同构群

数学季刊 ›› 2012, Vol. 27 ›› Issue (1): 98-103.

U(4,Z)的自同构群

1. Department of Mathematics, Henan University of Technology 2. Department of Mathematics, China University of Mining and Technology

收稿日期:2010-03-01 出版日期:2012-03-30 发布日期:2023-04-07
作者简介:WANG Yu-lei(1979-), male, native of Nanyang, Henan, a lecturer of Henan University of Technology, Ph.D., engages in algebra.
基金资助:
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)

The Automorphism Group of U(4,Z)

1. Department of Mathematics, Henan University of Technology 2. Department of Mathematics, China University of Mining and Technology

Received:2010-03-01 Online:2012-03-30 Published:2023-04-07
About author:WANG Yu-lei(1979-), male, native of Nanyang, Henan, a lecturer of Henan University of Technology, Ph.D., engages in algebra.
Supported by:
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)

摘要/Abstract

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, a^b=a^-1, [a,c]= [b,c]=1; (iii) K/InnG≌=Z×Z×Z.

关键词: upper unitriangular matrix groups, general linear groups, automorphism groups

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, a^b=a^-1, [a,c]= [b,c]=1; (iii) K/InnG≌=Z×Z×Z.

Key words: upper unitriangular matrix groups, general linear groups, automorphism groups

中图分类号:

O152

王玉雷, 孙大为, 王志俊. U(4,Z)的自同构群[J]. 数学季刊, 2012, 27(1): 98-103.

WANG Yu-lei, SUN Da-wei, WANG Zhi-jun. The Automorphism Group of U(4,Z) [J]. Chinese Quarterly Journal of Mathematics, 2012, 27(1): 98-103.

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