2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/62754Chevalley's theorem and it's converse, the Sheppard-Todd theorem, assert that finite reflection groups are distinguished by the fact that the ring of invariant polynomials is freely generated. We show that in the Euclidean case, a weaker condition suffices to characterize finite reflection groups, namely that a freely-generated polynomial subring is closed with respect to the gradient product.Differential GeometryGroup TheoryRings and Algebras20H15 14L24 53B21text