Generators for the Euclidean Picard Modular Groups

2010/06/16 by Tiehong Zhao, Zhao, Tiehong · 2 citations
Mathematics · #32M05 (Primary) 22E40 #32M15 (Secondary) #FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #math.GR #math.GT #msc:22E40 #msc:32M05 #msc:32M15

paper · pdf · doi:10.48550/arxiv.1006.3331

25 pages,12 figures

arxiv created 2010/06/19 · arxiv updated 2010/06/24

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

Cited by

• Generators of the Gauss-Picard modular groups in three complex dimensions
• Generators of the sister of Euclidean Picard modular group

Related

• Generators of the Gauss-Picard modular groups in three complex dimensions
• Generators of a Picard modular group in two complex dimensions
• Generators of the sister of Euclidean Picard modular group
• Presentations for the Euclidean Picard modular groups
• Generators of Picard modular groups