 A Schottky group is any Kleinian group that can be constructed like this.By work of , a finitely generated Kleinian group is Schottky if and only if it is finitely generated, free, has nonempty domain of discontinuity, and all non-trivial elements are loxodromic.A fundamental domain for the action of a Schottky group "G" on its regular points Ω("G") in the Riemann sphere is given by the exterior of the Jordan curves defining it.