We prove that every nonabelian free group has a finitely generated isolated subgroup which is not separable in the class of nilpotent groups. This enables us to give a negative answer to the following question by D.I. Moldavanskii in the "Kourovka Notebook": Is it true that any finitely generated $p'$--isolated subgroup of a free group is separable in the class of finite $p$--groups?
Categories: math.GR