Abstract
Previously, N. Khisamiev proved that all {ie172-1} Abelian torsion-free groups are {ie172-2}. We prove that for the class of nilpotent torsion-free groups, the situation is different: even the quotient group F of a {ie172-3} nilpotent group of class 2 by its periodic part may fail to have a {ie172-4}.
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Translated fromAlgebra i Logika, Vol. 35, No. 3, pp. 308–313, May–June, 1996.
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Latkin, I.V. The arithmetical hierarchy of nilpotent torsion-free groups. Algebr Logic 35, 172–175 (1996). https://doi.org/10.1007/BF02367215
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DOI: https://doi.org/10.1007/BF02367215