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Journal of Lie Theory 11 (2001), No. 2, 491--503
Copyright Heldermann Verlag 2001

Some Examples of Discrete Groups and Hyperbolic Orbifolds of Infinite Volume

Elena Klimenko
Dept. of Mathematics, Technion, Israel Institute of Technology, Haifa 32000, Israel

We study the class of two-generator subgroups of PSL(2, C) with real parameters which was introduced recently by Gehring, Gilman, and Martin. We give criteria for discreteness of non-elementary and non-Fuchsian groups of this class that are generated by two hyperbolic elements. We construct all hyperbolic orbifolds uniformized by the discrete groups of such type. The orbifolds described are of infinite volume.

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