摘要: 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。
Abstract:
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.