2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/71543We prove that every free metabelian non--cyclic group has a finitely generated isolated subgroup which is not separable in the class of nilpotent groups. As a corollary we prove that for every prime number $p$ an arbitrary free metabelian non--cyclic group has a finitely generated $p'$--isolated subgroup which is not $p$--separable.7 pagesGroup Theory20F16; 20F14; 20F10text