2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/159374The interplay between the Hamilton-Jacobi theory of orthogonal separation of variables and the theory of group actions is investigated based on concrete examples.This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/Mathematical PhysicsDifferential GeometryExactly Solvable and Integrable Systemstext