单位上三角矩阵群的多项式自同构  

The Polynomial Automorphisms of the Unitriangular Matrices

作　　者：张凯燕 雒晓良 ZHANG Kaiyan;LUO Xiaoliang(School of Mathematics and Statistics,Taiyuan Normal University,Jinzhong Shanxi 030619,China)

机构地区：[1]太原师范学院数学与统计学院,山西晋中030619

出　　处：《太原师范学院学报（自然科学版）》2024年第1期28-31,共4页Journal of Taiyuan Normal University:Natural Science Edition

基　　金：山西省教育厅科技创新项目(2020L0518).

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.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 matrices 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 

分 类 号：O152.1[理学—数学]