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Geometry of Neumann subgroups

Part of: Structure and classification of infinite or finite groups

Published online by Cambridge University Press:  09 April 2009

Ravi S. Kulkarni
Ravi S. Kulkarni
Affiliation:
Department of Mathematics, City University of New York33 W. 42nd Street New York, New York 10036–8099, U.S.A.
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Abstract

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A Neumann subgroup of the classical modular group is by definition a complement of a maximal parabolic subgroup. Recently Neumann subgroups have been studied in a series of papers by Brenner and Lyndon. There is a natural extension of the notion of a Neumann subgroup in the context of any finitely generated Fuchsian group Γ acting on the hyperbolic plane H such that Γ/H is homeomorphic to an open disk. Using a new geometric method we extend the work of Brenner and Lyndon in this more general context.

MSC classification

Secondary: 20E28: Maximal subgroups
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 47 , Issue 3 , December 1989 , pp. 350 - 367
Copyright
Copyright © Australian Mathematical Society 1989

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