All discrete RP groups with non-$π$-loxodromic generators

E. Klimenko; N. Kopteva

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All discrete RP groups with non-$π$-loxodromic generators

E. Klimenko·N. Kopteva

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Abstract

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.

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BibTeX RIS

E. Klimenko, N. Kopteva. 2005-08-17. All discrete RP groups with non-$π$-loxodromic generators. https://arxiv.org/abs/math/0301346

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