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.

DOI:
https://doi.org/10.1090/S0002-9947-96-01606-6

MathSciNet review:
1348863

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Abstract | References | Similar Articles | Additional Information

Abstract: A maximal non-elementary Fuchsian subgroup of a Bianchi group has an invariant circle or straight line under its linear fractional action on the complex plane, to which is associated a positive integer , 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

Email:
james@math.psu.edu

**C. Maclachlan**

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

Email:
cmac@maths.aberdeen.ac.uk

DOI:
https://doi.org/10.1090/S0002-9947-96-01606-6

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