Abstract
We prove that every free nonabelian group has a finitely generated isolated subgroup 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 every finitely generated $$p\prime $$ -isolated subgroup of a free group is separable in the class of finite p-groups?
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