The Automorphism Group of U（4,Z）  

作　　者：WANG Yu-lei SUN Da-wei WANG Zhi-jun 

机构地区：[1]Department of Mathematics,Henan University of Technology,Zhengzhou 450001,China [2]Department of Mathematics,China University of Mining and Technology,Xuzhou 221116,China

出　　处：《Chinese Quarterly Journal of Mathematics》2012年第1期98-103,共6页数学季刊（英文版）

基　　金：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：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≌=G_1×D_8×Z_2,where G_1=(a,b,c|a^4=b^2=c^2=1,a^b=a^(-1),[a,c]= [b,c]=1 ;(iii) K/Inn G≌=Z×Z×Z.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.

关 键 词：upper unitriangular matrix groups general linear groups automorphism groups 

分 类 号：O153.3[理学—数学]