Generators for the Euclidean Picard Modular Groups

Details Generators for the Euclidean Picard Modular Groups Generators for the Euclidean Picard Modular Groups

2010-06-16

arxiv.org/abs/1006.3331v2

Mathematics

Group Theory

25 pages,12 figures

Scientific paper

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 the relations of the isotropy subgroup by analysis of the combinatorics of the fundamental domain in Heisenberg group.

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