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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Generators for the Euclidean Picard modular groups


Author: Tiehong Zhao
Journal: Trans. Amer. Math. Soc. 364 (2012), 3241-3263
MSC (2010): Primary 22E40; Secondary 32M15, 32Q45
Published electronically: November 7, 2011
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Abstract: The goal of this article is to show that five explicitly given transformations, a rotation, two screw Heisenberg rotations, a vertical translation and an involution generate the Euclidean Picard modular groups with coefficient in the Euclidean ring of integers of a quadratic imaginary number field. We also obtain a presentation of the isotropy subgroup fixing infinity by analysis of the combinatorics of the fundamental domain in the Heisenberg group.


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Additional Information

Tiehong Zhao
Affiliation: Institut de Mathématiques, Université Pierre et Marie Curie, 4, place Jussieu, F-75252 Paris, France
Email: zhao@math.jussieu.fr

DOI: http://dx.doi.org/10.1090/S0002-9947-2011-05524-8
PII: S 0002-9947(2011)05524-8
Received by editor(s): July 6, 2010
Received by editor(s) in revised form: November 25, 2010
Published electronically: November 7, 2011
Additional Notes: The author was supported by the China-funded Postgraduates Studying Abroad Program for Building Top University.
Article copyright: © Copyright 2011 American Mathematical Society