The Unipotency of Linear Groups Generated by Matrices with Primitive  Elements Contain no more than Six Jorden Blocks

YANG Xin-song; MA Chang

doi:10.15938/j.jhust.2019.01.021

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The Unipotency of Linear Groups Generated by Matrices with Primitive  Elements Contain no more than Six Jorden Blocks

更新时间：2026-08-31

- The Unipotency of Linear Groups Generated by Matrices with Primitive  Elements Contain no more than Six Jorden Blocks
- Vol. 24, Issue 1, Pages: 124-131(2019)
- 作者机构：
  
  哈尔滨理工大学理学院,黑龙江,哈尔滨,150080
- 作者简介：
- 基金信息：
- DOI：10.15938/j.jhust.2019.01.021
  CLC： O1533
- Published：2019
- 稿件说明：
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YANG Xin-song, MA Chang. The Unipotency of Linear Groups Generated by Matrices with Primitive  Elements Contain no more than Six Jorden Blocks[J]. 2019, 24(1): 124-131.
DOI：

YANG Xin-song, MA Chang. The Unipotency of Linear Groups Generated by Matrices with Primitive  Elements Contain no more than Six Jorden Blocks[J]. 2019, 24(1): 124-131. DOI： 10.15938/j.jhust.2019.01.021.

摘要

摘要:针对两个幂单矩阵生成的矩阵是否幂单的问题，先利用矩阵对数工具得到了自由群生成元的新的组合性质。从这些新的组合性质出发，证明了由一个若当块不高于二阶和若当块不高于五阶矩阵生成的群，在本原元若当块不高于六阶的情况下，当本原元素均幂单时，生成的群是幂单群。这样就可以得出线性表示像满足同样条件的自由群也是幂单群。

Abstract

Abstract:In order to solve the problem of whether the matrices generated by two unipotent matrices are unipotency

a new combinatorial property of generators of free groups is obtained by using the matrix logarithmic tool。From the point of the combination of these new properties

it is proved that a Jordan block is not higher than two and if the order when the block is not higher than five order matrix generated group

when the block is not higher than six order

the primitive element is unipotency

the group generated is unipotent group

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Related Institution

School of Sciences, Harbin University of Science and Technology

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