2003/01/31 by E. Klimenko, N. Kopteva
Mathematics · #math.GR #msc:30F40 #msc:57S30 #msc:20H10
published as Int. J. Algebra Comput., 15 (2005), no. 3, 577-618 · 43 pages, 26 figures; minor changes; Table 2 is corrected
arxiv created 2005/08/17 · arxiv updated 2009/11/30
In this paper we give necessary and sufficient conditions for discreteness of a group generated by a hyperbolic element and an elliptic one of odd order. This completes the classification of discrete groups with non-π-loxodromic generators in the class of two-generator groups with real parameters. The criterion is given also as a list of all parameters that correspond to discrete groups. An interesting corollary of the result is that the group of the minimal known volume hyperbolic orbifold has real parameters.