2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/101290The singly periodic genus-one helicoid was in the origin of the discovery of the first example of a complete minimal surface with finite topology but infinite total curvature, the celebrated Hoffman-Karcher-Wei's genus one helicoid. The objective of this paper is to give a uniqueness theorem for the singly periodic genus-one helicoid provided the existence of one symmetry.12 pages, 6 figuresDifferential GeometryPrimary 53A10; Secondary 53C42text