2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210067We show that any two elements of the pure braid group either commute or generate a free group, settling a question of Luis Paris. Our proof involves the theory of 3-manifolds and the theory of group actions on trees.7 pagesGeometric TopologyGroup Theory20F36; 20F28Two-generator subgroups of the pure braid grouptext