Mbius群的离散性

On the discreteness of Mbius groups

令G为扩充复平面上的一非初等M bius群,g0为任一斜驶型M bius变换.本文建立了G离散的一个充分条件:如果G中任意元g和g0生成的群离散,则G离散.这一结果改进了由Jrgensen建立的著名的离散判别准则.

<Abstrcat>Let G be a nonelementary Mbius group acting on the extended plane and g0 be a loxodromic type Mbius transformation.In this paper,we show that G is discrete if for each g∈G the group <g,g0> is discrete.This improves the wellknown discreteness criteria established by Jrgensen.