Abstract
It is proved that divisible groups and only these groups are absolutely closed (with respect to the operator of dominion) in the class of 2-step nilpotent torsion-free groups. It is established that the additive group of the rationals is 1-closed in an arbitrary quasivariety of nilpotent torsion-free groups and 3-closed in an arbitrary quasivariety of 2-step nilpotent torsion-free groups.
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Original Russian Text © S. A. Shakhova, 2015, published in Matematicheskie Zametki, 2015, Vol. 97, No. 6, pp. 936–941.
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Shakhova, S.A. Absolutely closed groups in the class of 2-step nilpotent torsion-free groups. Math Notes 97, 946–950 (2015). https://doi.org/10.1134/S0001434615050302
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DOI: https://doi.org/10.1134/S0001434615050302