三维非初等离散Mobius群的必要条件

Necessary Condition of Nonclementary Discrete Mobius Groups in R￣3

本文利用Ｃｌｉｆｆｏｒｄ矩阵及三维Ｍｏｂｕｓ变换的分类及判别法研究了三维Ｍｏｂｉｕｓ群．得到了：三维Ｍｏｂｉｕｓ变换ｆ和ｇ生成非初等离散群且ｆ是抛物或双曲元素时的必要条件：｜ｔｒ￣２－４｜＋｜ｔｒ［ｆ，ｇ］－２｜≥１．并由此推导出几个重要的结果．

In this paper,the author has studied 3-dimentional Mobius groups bymeans of Clifford matrices and Classincation and Identiflcation of Mobiustransformations in R￣3,obtained that the three-dimentional Mobius transfor-mations f and g generate a discrete nonelementary group and f is parabolic orhyperbolic, then |tr￣2(f)-4|+|tr[f,g]-2|≥1.In addition,the paperdiduces several importment results.