loxodrome

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_.

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。