二维Mbius子群的两个离散准则  

Two new discreteness criterions for two dimensional Mbius subgroups

作　　者：熊寿遥[1] 王仙桃[2] 

机构地区：[1]湖南大学数学与计量经济学院,湖南长沙410082 [2]湖南师范大学数学与计算机科学学院,湖南长沙410081

出　　处：《黑龙江大学自然科学学报》2004年第3期12-14,共3页Journal of Natural Science of Heilongjiang University

基　　金：国家自然科学基金(10271043)

摘　　要：关于二维Mbius群和高维Mbius群的离散性已有许多讨论,并得到很多结果,继续讨论二维Mbius群的离散问题:首先定义GSL(2,C)的子集合G_h(或G_p),即与G中斜驶元素h(或抛物元素p)共轭的所有元素构成的集合;然后建立由G_h(或G_p)中两元生成子群的离散性来决定G的离散性的两个结果,它们是已有相关结果的推广。There are a lot of discussions about the discreteness of 2-dimensional M(?)bius groups and higher dimensional M(?)bius groups, and many results have been obtained. The discreteness of 2-dimensional Mbius groups is further considered. Firstly, the authors define two new subsets G_h(or G_p) of G, which consists of the elements being conjugate to loxodromic element h(or parabolic element p) in G; then two new discreteness criterions for G by use of the discreteness of subgroups generated by two elements in G_h(or G_p) are obtained, which generalizes all existing results on this line.

关 键 词：斜驶元素 抛物元素 离散准则 非初等性 

分 类 号：O174.51[理学—数学]