On the separability of subgroups of nilpotent groups by root classes of groups

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On the separability of subgroups of nilpotent groups by root classes of groups

Sokolov, Evgeny Victorovich

Journal of group theory, 07/2023, Volume: 26, Issue: 4

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Suppose that 𝒞 is a class of groups consisting only of periodic groups and is the set of prime numbers that do not divide the order of any element of a 𝒞-group. It is easy to see that if a subgroup 𝑌 of a group 𝑋 is 𝒞-separable in this group, then it is -isolated in 𝑋. Let us say that 𝑋 has the property if all of its -isolated subgroups are 𝒞-separable. We find a condition that is sufficient for a nilpotent group 𝑁 to have the property provided 𝒞 is a root class. We also prove that if 𝑁 is torsion-free, then the indicated condition is necessary for this group to have

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