标准型不高于五阶若当块矩阵群的幂单性

The Unipotency of Linear Groups Generated by Matrices with Jordan Normal Blocks of Size at Most Five

根据组合群理论,使用初等方法证明了标准型不含五阶以上若当块的矩阵群在某生成元标准型不含三阶若当块及更高阶若当块时是幂单的,得到了一般二元生成自由群幂单的判定条件,推广了幂单性的已有结论 .

According to the theory of combination group,in this paper we will by elementary method prove that the linear group whose primitive elements consist Jordan normal blocks of size at most five is unipotent when the standard form of a certain generator don＇t consist Jordan normal blocks of size at three or higher size. We will also get a decision condition of the unipotency of free groups generated by two elements and develop existing conclusion of the unipotency.