Abstract
Considering a group with unique roots (i.e., an R-group), we give a sufficient condition for the existence of a positive (constructive) enumeration with respect to which the isolator of the commutant is computable. Basing on it, we prove the constructivizability of an R-group that admitting a positive enumeration for which the dimension of the commutant is finite. We obtain a necessary and sufficient condition of constructivizability for a torsion-free nilpotent group for which the dimension of the commutant is finite.
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Original Russian Text Copyright © 2012 Khisamiev N.G.
The author was supported by the Scientific-Technical Programs and Projects of the Science Committees of the Ministry of Education and Science of the Republic of Kazakhstan (Grants 0726/GF and 2012–2014.)
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Ust’-Kamenogorsk. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 53, No. 5, pp. 1133–1146, September–October, 2012.
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Khisamiev, N.G. On positive and constructive groups. Sib Math J 53, 906–917 (2012). https://doi.org/10.1134/S0037446612050151
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DOI: https://doi.org/10.1134/S0037446612050151