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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 684594, 5 pages
http://dx.doi.org/10.1155/2014/684594
Research Article

Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups

1College of Applied Mathematics, Hunan University, Changsha 410082, China
2College of Mathematics and Computation Science, Wuyi University, Jiangmen 529020, China

Received 21 March 2014; Accepted 5 May 2014; Published 18 May 2014

Academic Editor: Luigi Rodino

Copyright © 2014 Huani Qin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We obtain an analogue of Jørgensen's inequality in quaternionic hyperbolic space. As an application, we prove that if the r-generator quaternionic Kleinian group satisfies I-condition, then its algebraic limit is also a quaternionic Kleinian group. Our results are generalizations of the counterparts in the n-dimensional real hyperbolic space.