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GENERATORS FOR THE EUCLIDEAN PICARD MODULAR GROUPS

By Tiehong Zhao

Abstract

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. 1

Year: 2013
OAI identifier: oai:CiteSeerX.psu:10.1.1.308.9477
Provided by: CiteSeerX
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