2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/77187In the first part, we prove that the dominion (in the sense of Isbell) of a subgroup of a finitely generated nilpotent group is trivial in the category of all nilpotent groups. In the second part, we show that the dominion of a subgroup of a finitely generated nilpotent group of class two is trivial in the category of all metabelian nilpotent groups.Plain TeX, 15 pp. Typos corrected, added details to some proofs. Final versionGroup Theory08B25; 20F18 (primary) 20E10 (secondary)text