本原元只含不高于六阶若当块矩阵群的幂单性  

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

作　　者：杨新松 马畅 YANG Xin-song;MA Chang(Harbin University of Science and Technology,Harbin 150080,China)

机构地区：[1]哈尔滨理工大学理学院,黑龙江哈尔滨150080

出　　处：《哈尔滨理工大学学报》2019年第1期124-131,共8页Journal of Harbin University of Science and Technology

基　　金：国家自然科学基金(11871181)

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。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.

关 键 词：幂单群 本原元 自由群 群表示 

分 类 号：O153.3[理学—数学]