Computational Methods and Function Theory 5 (2005), No. 2, 409--430
Copyright Heldermann Verlag 2005
Changjun Li
changjunli7921@hotmail.com , Department of Mathematics, Ocean University of China, 23 Hong Kong, East Road, 266071 Qingdao, China.
Makito Oichi
smohiti@ipc.shizuoka.ac.jp , Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Surugaku, 422-8529 Shizuoka, Japan.
Hiroki Sato
smhsato@ipc.shizuoka.ac.jp , Department of Mathematics, Faculty of Science, Shizuoka University, 836 Ohya, Surugaku, 422-8529 Shizuoka, Japan.
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.
Keywords: Jørgensen's inequality, Jørgensen number, Jørgensen group, Kleinian group, Poincaré's polyhedron theorem.
MSC 2000: Primary 30F40; Secondary 20H10, 32G15.
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