整数环上上三角幺幂子群的自同构

摘要

Let U be the upper triangular unipotent subgroup of the general linear group GL(n+1,Z). In this paper we explicitly describe the automorphism group of U. We prove that any automorphism of U is uniquely expressed as a product of graph, diagonal, inner, extremal and central automorphisms when n≥3.When n=1,2, we also discuss the automorphism group of U.%设U是整数环Z上一般线性群GL(n+1,Z)的上三角幺幂子群,讨论U的自同构，证明了当n≥3时，U的任一个自同构都可以唯一地表示为图自同构、对角自同构、内自同构、极自同构、中心自同构的乘积;当n=1,2时，对U的自同构也进行了讨论.