Abstract
本文运用λ-矩阵的相关理论和常系数线性齐次递归关系的求解方法，对特殊线性群SL(2,R) 的有限Abelian子群进行了研究，给出了其任意阶循环群的结构，即2阶矩阵方程： 且 ，其中 的全部解。进一步，我们希望通过探讨各阶循环群生成元的交换性来确定 SL(2,R) 的有限Abelian子群结构。 In this paper, we study the finite Abelian subgroup of special linear group SL(2,R) by using the eigenvalue theory of λ-matrix and the solution method of constant coefficient linear homogeneous recursive relations. We get the structure of cyclic group for arbitrary order n of SL(2,R) , that is to say, all the solutions of the 2 order matrix equation: and ( ) are given out. Furthermore, we hope to determine the structure of finite Abelian subgroup of special linear group SL(2,R) by discussing the commutativity between generators of arbitrary order cyclic group.
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