2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/163475We say that an algebraic group $G$ over a field is anti-affine if every regular function on $G$ is constant. We obtain a classification of these groups, with applications to the structure of algebraic groups in positive characteristics, and to the construction of many counterexamples to Hilbert's fourteenth problem.Prior work of Carlos Sancho de Salas acknowledged, additional minor changes,Algebraic GeometryGroup Theory14K05, 14L10, 14L15, 20G15text