Dihedral groups are of schottky type

All Fuchsian Schottky groups are classical Schottky groups

Not all Schottky groups of Möbius transformations are classical Schottky groups. In this paper we show that all Fuchsian Schottky groups are classical Schottky groups, but not necessarily on the same set of generators. AMS Classification 20H10; 30F35, 30F40

Calculations of Dihedral Groups Using Circular Indexation

‎In this work‎, ‎a regular polygon with $n$ sides is described by a periodic (circular) sequence with period $n$‎. ‎Each element of the sequence represents a vertex of the polygon‎. ‎Each symmetry of the polygon is the rotation of the polygon around the center-point and/or flipping around a symmetry axis‎. ‎Here each symmetry is considered as a system that takes an input circular sequence and g...

Kleinian groups of small Hausdorff dimension are classical Schottky groups

Let H be the hyperbolic 3-space. A subgroup Γ of PSL(2,C) = Iso(H) is called a Kleinian group if it is discrete. Let x ∈ H. The orbit of x under action of Γ is denoted by Γx. The limit set ΛΓ of Γ is definited as ΛΓ = Γx ∩ ∂H. By definition, ΛG is smallest closed Γ-invariant subset of ∂H. The group Γ is called second kind if ΛΓ 6= ∂H, otherwise it is said to be first kind. The set ΩΓ = ∂H 3 − Λ...

Dihedral Groups

Limits of Dihedral Groups

We give a characterization of limits of dihedral groups in the space of finitely generated marked groups. We also describe the topological closure of dihedral groups in the space of marked groups on a fixed number of generators.