单位上三角矩阵群的多项式自同构
The Polynomial Automorphisms of the Unitriangular Matrices
张凯燕 1雒晓良1
作者信息
- 1. 太原师范学院数学与统计学院,山西晋中 030619
- 折叠
摘要
幂零群是群论中的一类重要研究对象,其中单位上三角矩阵群由于其幂零类为n-1,在幂零群中有极为重要的地位.而多项式自同构由于其多项式特性,更是受到群论学者的特别关注,本文通过换位子计算得出有限域上的3阶单位上三角矩阵群的每个多项式自同构一定是内自同构.
Abstract
The nilpotent groups is an important research object in the group theory,in which the upper unitriangular matrix group holds a more important position in the nilpotent groups due to its class is n-1.The polynomial automorphisms of the given groups have been widely concerned because of its properties.This paper proves that every the polynomial automorphisms of the unitriangular matri-ces of order 3 over a finite field is necessarily inner automorphisms.
关键词
多项式自同构/单位上三角矩阵群/内自同构Key words
polynomial automorphism/upper unitriangular matrices/inner automorphism引用本文复制引用
基金项目
山西省教育厅科技创新项目(2020L0518)
出版年
2024
NETL
NSTL
万方数据