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

Valerij G. Bardakov
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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 $p'$--isolated subgroup of a free group is separable in the class of finite $p$--groups?

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Valerij G. Bardakov. 2004-05-11. On D. I. Moldavanskii's question about $p$-separable subgroups of a free group. https://arxiv.org/abs/math/0404292

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