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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Qin, Huani Jiang, Yueping and Cao, Wensheng 2014. Jørgensen’s Inequality and Algebraic Convergence Theorem in Quaternionic Hyperbolic Isometry Groups. Abstract and Applied Analysis, Vol. 2014, p. 1.

    Fu, Xi 2013. Discreteness and Convergence of Complex Hyperbolic Isometry Groups. Abstract and Applied Analysis, Vol. 2013, p. 1.



  • DOI:
  • Published online: 02 August 2012

Let {Gr,i} be a sequence of r-generator subgroups of U(1,n; ℂ) and Gr be its algebraic limit group. In this paper, two algebraic convergence theorems concerning {Gr,i} and Gr are obtained. Our results are generalisations of their counterparts in the n-dimensional sense-preserving Möbius group.

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1.B. N. Apanasov, Conformal geometry of discrete groups and manifolds (Walter de Gruyter, Berlin, Germany, 2000).

3.W. Cao and X. Wang, Discreteness criteria and algebraic convergence theorem for subgroups in PU(1, n; ℂ), Proc. Japan Acad. 82 (2006), 4952.

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9.G. J. Martin, On discrete Möbius groups in all dimensions, Acta Math. 163 (1989), 253289.

10.J. P. Navarrete, On the limit set of discrete subgroups of PU(2, 1), Geometriae Dedicata 122 (2006), 113.

11.X. Wang, Algebraic convergence theorems of n-dimensional Kleinian groups, Isr. J. Math. 162 (2007), 221233.

12.X. Wang and W. Yang, Discreteness criteria of Möbius groups of high dimensions and convergence theorem of Kleinian groups, Adv. Math. 159 (2001), 6882.

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Glasgow Mathematical Journal
  • ISSN: 0017-0895
  • EISSN: 1469-509X
  • URL: /core/journals/glasgow-mathematical-journal
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