Chinese Quarterly Journal of Mathematics ›› 2012, Vol. 27 ›› Issue (1): 98-103.

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The Automorphism Group of U(4,Z) 

  

  1. 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)

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/InnG≌=Z×Z×Z.


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

CLC Number: