On D. I. Moldavanskij’s question on \(p\)-separable subgroups of a free group. (Russian, English) Zbl 1058.20027
Sib. Mat. Zh. 45, No. 3, 505-509 (2004); translation in Sib. Math. J. 45, No. 3, 416-419 (2004).
Summary: 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 Problem 15.60 of the Kourovka notebook [V. D. Mazurov and E. I. Khukhro (eds.), The Kourovka notebook. Unsolved problems in group theory, Novosibirsk (2002; Zbl 0999.20001)] posed by D. I. Moldavanskij: Is it true that every finitely generated \(p\)-isolated subgroup of a free group is separable in the class of finite \(p\)-groups?
MSC:
| 20E05 | Free nonabelian groups |
| 20E07 | Subgroup theorems; subgroup growth |
| 20D15 | Finite nilpotent groups, \(p\)-groups |
