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On Conjugacy Classes of Congruence Subgroups of PSL(2, R)

Published online by Cambridge University Press:  01 February 2010

C. J. Cummins
C. J. Cummins
Affiliation:
Department of Mathematics and Statistics, Concordia University, Montréal, Québec, Canada, [email protected]

Abstract

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Let G be a subgroup of PSL(2, R) which is commensurable with PSL(2, Z). We say that G is a congruence subgroup of PSL(2, R) if G contains a principal congruence subgroup /overline Γ(N) for some N. An algorithm is given for determining whether two congruence subgroups are conjugate in PSL(2, R). This algorithm is used to determine the PSL(2, R) conjugacy classes of congruence subgroups of genus-zero and genus-one. The results are given in a table.

Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 12 , 2009 , pp. 264 - 274
Copyright
Copyright © London Mathematical Society 2009

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