M变换中的n阶循环群判定

摘要

用二阶方阵的幂运算取代MM(o)bius变换的迭代运算,借助2个常数△和δ以及2个与△,δ相关的数列△n,δn,证明了任何二阶方阵n次幂后的4个元素均可用△n,δn来表达.进而得到M变换为n阶循环群的判定式.%By replacing iterative computation in Mobius transformation (MT) with computation of powers of 2 × 2 square matrix, and by using two constants A and 5 as well as two seguences △n ,δn related to △, S, a formula of the n of a 2 × 2 square matrix was proved in terms of Δn and δn, and a criterion of MT being a cyclic group of order n was given.