2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/210191This is the third paper in a sequence on Krull dimension for limit groups, answering a question of Z. Sela. We give generalizations of the well known fact that a nontrivial commutator in a free group is not a proper power to both graphs of free groups over cyclic subgroups and freely decomposable groups. None of the paper is specifically about limit groups.Consistent with other in the series, I hope. No major changes. New titleGroup Theory20F65 (Primary); 20E05, 20E06 (Secondary)text