On D. I. Moldavanskii's question about $p$-separable subgroups of a free group

Abstract

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 $p^{\prime }$--isolated subgroup of a free group is separable in the class of finite $p$--groups?

5 pages, to appear in Siberian Mathematical Journal