Computational Methods and Function Theory

, Volume 5, Issue 2, pp 409–430

Jørgensen Groups of Parabolic Type I (Finite Case)


DOI: 10.1007/BF03321107

Cite this article as:
Li, C., Oichi, M. & Sato, H. Comput. Methods Funct. Theory (2006) 5: 409. doi:10.1007/BF03321107


In this paper we consider extreme discrete two-generator groups (Jørgensen groups) of parabolic type — finite case — for Jørgensen’s inequality. There are exactly 16 Jørgensen groups, including the modular group, the Picard group and the figure-eight knot group, in this case. Nine of them are Kleinian groups of the first kind and seven of them are Kleinian groups of the second kind.


Jørgensen’s inequality Jørgensen number Jørgensen group Kleinian group Poincaré’s polyhedron theorem 

2000 MSC

30F40 20H10 32G15 

Copyright information

© Heldermann  Verlag 2005

Authors and Affiliations

  1. 1.Department of MathematicsOcean University of ChinaQingdaoChina
  2. 2.Department of Mathematics, Faculty of ScienceShizuoka UniversitySurugakuJapan

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