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Fuchsian Subgroups of Bianchi Groups

Authors: D. G. James and C. Maclachlan
Journal: Trans. Amer. Math. Soc. 348 (1996), 1989-2002
MSC (1991): Primary 11F06; Secondary 11E08, 11E12, 20H10.
MathSciNet review: 1348863
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Abstract: A maximal non-elementary Fuchsian subgroup of a Bianchi group $PSL(2,O_d)$ has an invariant circle or straight line under its linear fractional action on the complex plane, to which is associated a positive integer $D$, the discriminant, which, in turn, is an invariant of the wide commensurability class of the Fuchsian subgroup. In this paper, for all Bianchi groups, we classify the conjugacy classes of these maximal Fuchsian subgroups by determining the number with given discriminant.

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Additional Information

D. G. James
Affiliation: Department of Mathematics, Pennsylvania State University, University Park, Pennsylvania 16802

C. Maclachlan
Affiliation: Department of Mathematical Sciences, University of Aberdeen, Old Aberdeen, Aberdeen AB9 2TY, Scotland

Received by editor(s): November 11, 1994
Received by editor(s) in revised form: July 6, 1995
Additional Notes: The first author partially supported by NSA and NSF grants
Both authors would like to thank the Mathematics Department of the University of Auckland for its hospitality
Article copyright: © Copyright 1996 American Mathematical Society