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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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