A Note on Discrete Groups
Stanley O. Juriaans, Severino C. Lima Neto, Antonio de A. E. Silva

TL;DR
This paper characterizes groups with a DF domain as those with a Double Dirichlet domain, describing their side-paring transformations and eigenvectors, with additional results on Kleinian and Fuchsian groups.
Contribution
It establishes an equivalence between DF domains and Double Dirichlet domains in groups, and details their geometric and algebraic properties.
Findings
Groups with DF domains are exactly those with Double Dirichlet domains.
Such groups not fixing infinity share a common eigenvector.
Provides new insights into Kleinian and Fuchsian group structures.
Abstract
We prove that a group has a DF domain if and only if has a Double Dirichlet domain. We give a good describtion of the side-paring transformation of such groups. In particular, those not fixing infinity have a common eigenvector. We also give other results on Kleinian and Fuchsian groups.
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Taxonomy
TopicsGeometric and Algebraic Topology · Finite Group Theory Research · semigroups and automata theory
