Cirre Torres, Francisco JavierMonerri Molina, Alejandro José2025-12-232025-12-232022-01-01-978-1-4704-6025-9https://doi.org/10.1090/conm/776/15620https://hdl.handle.net/20.500.14468/31281We study finitely generated discrete groups of hyperbolic plane isometries (including those which reverse orientation) with non-compact orbit space. A presentation by generators and relations of this type of group is obtained. To that end, we use the geometrical properties of a fundamental region with a canonical form, and apply Macbeath’s classical theorem on presentations of groups of isometries of simply connected spaces. Our main result here is a complete version of a structure theorem stated without proof by Zieschang, Vogt and Coldewey in [9].eninfo:eu-repo/semantics/openAccess1204 Geometríacapítulo de libro978-1-4704-6776-0