Generators for the Euclidean Picard modular groups

Zhao, Tiehong

doi:10.1090/S0002-9947-2011-05524-8

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
DOI: https://doi.org/10.1090/S0002-9947-2011-05524-8
Published electronically: November 7, 2011
MathSciNet review: 2888244
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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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