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Torsion-free constructive nilpotent R p -groups

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Abstract

We consider a torsion-free nilpotent R p -group, the p-rank of whose quotient by the commutant is equal to 1 and either the rank of the center by the commutant is infinite or the rank of the group by the commutant is finite. We prove that the group is constructivizable if and only if it is isomorphic to the central extension of some divisible torsion-free constructive abelian group by some torsion-free constructive abelian R p -group with a computably enumerable basis and a computable system of commutators. We obtain similar criteria for groups of that type as well as divisible groups to be positively defined. We also obtain sufficient conditions for the constructivizability of positively defined groups.

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Authors and Affiliations

  1. East Kazakhstan State Technical University, Ust’-Kamenogorsk, Kazakhstan

    N. G. Khisamiev

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  1. N. G. Khisamiev
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Correspondence to N. G. Khisamiev.

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Original Russian Text Copyright © 2009 Khisamiev N. G.

The author was supported by the Kazakhstan Science Foundation (Grant 1.7.1–2).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 50, No. 1, pp. 222–230, January–February, 2009.

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Khisamiev, N.G. Torsion-free constructive nilpotent R p -groups. Sib Math J 50, 181–187 (2009). https://doi.org/10.1007/s11202-009-0020-9

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  • DOI: https://doi.org/10.1007/s11202-009-0020-9

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