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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)
  • Received : 2010.01.11
  • Published : 2012.01.31

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.

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Cited by

  1. ON DISCRETENESS OF MÖBIUS GROUPS vol.50, pp.3, 2013, https://doi.org/10.4134/BKMS.2013.50.3.747