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http://dx.doi.org/10.4134/BKMS.2012.49.1.057

DISCRETENESS BY USE OF A TEST MAP  

Li, Liulan (Department of Mathematics and Computational Science Hengyang Normal University)
Fu, Xi (Department of Mathematics Hunan Normal University)
Publication Information
Bulletin of the Korean Mathematical Society / v.49, no.1, 2012 , pp. 57-61 More about this Journal
Abstract
It is well known that one could use a fixed loxodromic or parabolic element of a non-elementary group $G{\subset}M(\bar{\mathbb{R}}^n)$ as a test map to test the discreteness of G. In this paper, we show that a test map need not be in G. We also construct an example to show that the similar result using an elliptic element as a test map does not hold.
Keywords
discreteness; non-elementary M$\ddot{o}$bius group; test map;
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