线性表示维数为9的自由群的幂单性  

The Unipotency of the Free Group with Linear Representation of Dimension 9

作　　者：杨新松 刁鑫 YANG Xin-song;DIAO Xin(School of Sciences, Harbin University of Science and Technology, Harbin 150080)

机构地区：[1]哈尔滨理工大学理学院,哈尔滨150080

出　　处：《哈尔滨理工大学学报》2021年第6期138-148,共11页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181).

摘　　要：利用组合群论的方法寻找本原元的性质,通过对不同Jordan标准形的讨论和对幂单矩阵性质的分析,并利用计算机软件进行辅助计算,找到可以使二元生成自由群在线性表示维数是9时成为幂单群的条件。对幂单性的已有结论进行了推广。By using the method of combinatorial group theory,the properties of primitives are found.By discussing different Jordan canonical forms and analyzing the properties of unipotent matrices,and by using computer software,the conditions that binary generated free groups which linear representation dimension are nine can be proved unipotent groups are found.The existing conclusions have been promoted.

关 键 词：本原元 幂单性 自由群 线性表示 

分 类 号：O153.3[理学—数学]