Abstract
Jørgensen’s inequality gives a necessary condition for a nonelementary two generator subgroup of \(SL(2, {\mathbb C})\) to be discrete. By embedding \(SL(2,{\mathbb C})\) into \(\hat U(1,1; {\mathbb H})\), we obtain a new type of Jørgensen’s inequality, which is in terms of the coefficients of involved isometries. We provide an example to show that this result gives an improvement over the classical Jørgensen’s inequality.
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Acknowledgement
This research was supported by Hunan Provincial Educational Department Science Foundation (No. 11c0050) and the Provincial Natural Science Foundation of Human, China (No. 12jj3006).
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WANG, H., JIANG, Y. & CAO, W. Notes on discrete subgroups of Möbius transformations. Proc Math Sci 123, 245–251 (2013). https://doi.org/10.1007/s12044-013-0120-0
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DOI: https://doi.org/10.1007/s12044-013-0120-0