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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Fuchsian Subgroups of Bianchi Groups
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by D. G. James and C. Maclachlan PDF
Trans. Amer. Math. Soc. 348 (1996), 1989-2002 Request permission


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
  • Email:
  • C. Maclachlan
  • Affiliation: Department of Mathematical Sciences, University of Aberdeen, Old Aberdeen, Aberdeen AB9 2TY, Scotland
  • Email:
  • 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
  • © Copyright 1996 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 348 (1996), 1989-2002
  • MSC (1991): Primary 11F06; Secondary 11E08, 11E12, 20H10
  • DOI:
  • MathSciNet review: 1348863