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Discreteness criteria forRP groups

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Abstract

Recently Gehring, Gilman, and Martin introduced an important class of two-generator groups with real parameters:\(\left\{ {\Gamma = \left\langle {f,g} \right\rangle \left| {f,g \in PSL(2,C);\beta ,\beta ^\prime ,\gamma \in R} \right.} \right\}\) whereβ=tr2 f−4,β′=tr2 g−4, and γ=tr(fgf −1 g −1)−2. The groups that belong to this class we callRP groups. We find criteria for discreteness ofRP groups generated by a hyperbolic element and an elliptic one of even order with intersecting axes.

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Author notes

  1. E. Klimenko

    Present address: Department of Mathematics, Northwestern University, 2033 Sheridan Road, 60208-2730, Evanston, IL, USA

Authors and Affiliations

  1. Department of Mathematics, Technion-Israel Institute of Technology, 32000, Haifa, Israel

    E. Klimenko

  2. Department of Mathematics, Heriot-Watt University, EH14 4AS, Edinburgh, Scotland

    N. Kopteva

Authors
  1. E. Klimenko
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  2. N. Kopteva
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Additional information

The research was partially supported by the Russian Foundation for Basic Research (Grant 99-01-00630).

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Klimenko, E., Kopteva, N. Discreteness criteria forRP groups. Isr. J. Math. 128, 247–265 (2002). https://doi.org/10.1007/BF02785427

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  • DOI: https://doi.org/10.1007/BF02785427

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