, Volume 5, Issue 2, pp 409-430
Date: 07 Mar 2013

Jørgensen Groups of Parabolic Type I (Finite Case)

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Abstract

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.

Partly supported by the Grants-in-Aid for Co-operative Research as well as Scientific Research, the Ministry of Education, Science, Sports and Culture, Japan.