On $p$-separability of subgroups of free metabelian groups
  We 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. 
Valerij G. Bardakov