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Classification of Maximal Fuchsian Subsgroups of Some Bianchi Groups

Published online by Cambridge University Press:  20 November 2018

L. Ya. Vulakh
L. Ya. Vulakh*
Affiliation:
Department of Mathematics, The Cooper Union, 51 As tor Place, New York, NY, USA 10003
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Abstract

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Let d = 1,2, or p, prime p ≡ 3 (mod 4). Let Od be the ring of integers of an imaginary quadratic field A complete classification of conjugacy classes of maximal non-elementary Fuchsian subgroups of PSL(2, Od) in PGL(2, Od) is given.

Keywords

11F0620H1011H50
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 34 , Issue 3 , 01 September 1991 , pp. 417 - 422
Copyright
Copyright © Canadian Mathematical Society 1991

References

1. Beardon, A. F., The Geometry of Discrete Groups. Springer-Verlag, New York, 1983.Google Scholar
2. Fine, B., Fuchsian subgroups of the Picard group, Can. J. Math. 28 (1976), 481–486.Google Scholar
3. Fine, B., Fuchsian embeddings in the Bianchi groups, Can. J. Math. 39 (1987), 1434–1445.Google Scholar
4. Maclachlan, C., Fuchsian subgroups of the groups PSL2(Od). In Durham Conference on Hyperbolic Geometry, London Math. Soc. Lecture Notes Series no. 112 (Cambridge University Press, 1986), 305–311.Google Scholar
5. Maclachlan, C. and Reid, A. W., Commensurability classes of arithmetic, Kleinian groups and their Fuchsian subgroups, Math. Proc. Camb. Phil. Soc. 102 (1987), 251–257.Google Scholar
6. Maclachlan, C. and Reid, A. W., Parametrizing Fuchsian subgroups of the Bianchi groups , preprint.Google Scholar
7. Margulis, G. A., Indefinite quadratic forms and unipotent flows on homogeneous spaces, C. R. Acad. Sci. Paris Ser. I Math. (10)304 (1987), 249–253.Google Scholar
8. Margulis, G. A., Discrete subgroups and ergodic theory. In Number Theory, trace formulas and discrete groups, symposium in honor of Atle Selberg held at the University of Oslo, Oslo, June 14-20, 1987. Edited by Karl Egil Aubert, Enrico Bombieri and Dorian Goldfeld, Academic Press, Inc., Boston, MA, 1989, 377- 398.Google Scholar
9. Swan, R. G., Generators and relations for certain special linear groups, Adv. in Math. 6 (1971), 1–77.Google Scholar
10. Ya. Vulakh, L., On minima of rational indefinite Hermitian forms ,, Ann. N. Y. Acad. Sci. 410( 1983), 99–106.Google Scholar
11. L. Ya. Vulakh, On minima of rational indefinite quadratic forms, J. Number Theory 21 (1985), 275–285.Google Scholar
12. Ya. Vulakh, L., On classification of arithmetic Fuchsian subgroups of PSL(2, o) , preprint.Google Scholar