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Normal subgroups of $PSL_2(Z[\sqrt {-3}])$

Author(s): Roger C. Alperin
Journal: Proc. Amer. Math. Soc. 124 (1996), 2935-2941.
MSC (1991): Primary 20E99, 20H25
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Abstract: We classify the normal subgroups of $PSL_2(Z[\sqrt {-3}])$ of index less than 960; they are all congruence subgroups.

References:

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Roger C. Alperin, Homology of $PSL_2(Z[\omega ])$, Comment. Math. Helv. 55 (1980), 364--377. MR 82f:20070

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Martin R. Bridson, Geodesics and curvature in metric simplicial complexes, Group Theory from a Geometrical Viewpoint, ICTP Trieste, World Scientific, 1991. MR 94c:57040

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Benjamin Fine, Algebraic theory of Bianchi groups, Marcel-Dekker, 1989. MR 90h:20002

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Benjamin Fine and Morris Newman, The normal subgroup structure of the Picard group, Trans. Amer. Math. Soc. 302 (1987), 769--786. MR 88d:20070

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J.-P. Serre, Le problème des groupes de congruence pour $SL_2$, Ann. of Math. 92 (1970), 489--527. MR 42:7671

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John Stallings, Non-positively curved triangles of groups, Group Theory from a Geometrical Viewpoint, ICTP trieste, World Scientific, 1991. MR 94b:20033

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Additional Information:

Roger C. Alperin
Affiliation: Department of Mathematics and Computer Science, San Jose State University, San Jose, California 95192
Email: alperin@math.sjsu.edu

DOI: 10.1090/S0002-9939-96-03429-6
PII: S 0002-9939(96)03429-6
Keywords: Triangle of groups, congruence subgroup, property FA
Received by editor(s): February 7, 1995
Additional Notes: The author's research was supported by NSA and NSF
Communicated by: Ronald M. Solomon
Copyright of article: Copyright 1996, American Mathematical Society

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