Abstract
Every element in PSL(2, ℂ) is elliptic, parabolic, or loxodromic. For the groups generated by two elliptic elements, sufficient discreteness conditions were obtained by Gehring, Maclachlan, Martin, and Rasskazov. In this article we establish sufficient discreteness conditions for the groups generated by two loxodromic elements and the groups generated by a loxodromic element and an elliptic element.
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Original Russian Text Copyright © 2013 Masley A.V.
The author was supported by the Russian Foundation for Basic Research (Grant 13-01-00513) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1414.2012.1).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 54, No. 5, pp. 1069–1086, September–October, 2013.
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Masley, A.V. Sufficient discreteness conditions for 2-generator subgroups in PSL(2, ℂ). Sib Math J 54, 857–870 (2013). https://doi.org/10.1134/S0037446613050108
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DOI: https://doi.org/10.1134/S0037446613050108