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单位上三角矩阵群的多项式自同构

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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 Polynomial Automorphisms of the Unitriangular Matrices
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.

polynomial automorphismupper unitriangular matricesinner automorphism

张凯燕、雒晓良

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太原师范学院数学与统计学院,山西晋中 030619

多项式自同构 单位上三角矩阵群 内自同构

山西省教育厅科技创新项目

2020L0518

2024

太原师范学院学报(自然科学版)
太原师范学院

太原师范学院学报(自然科学版)

影响因子:0.127
ISSN:1672-2027
年,卷(期):2024.23(1)
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