Abstract
We find criteria for the computability (constructivizability) of torsion-free nilpotent groups of finite dimension. We prove the existence of a principal computable enumeration of the class of all computable torsion-free nilpotent groups of finite dimension. An example is constructed of a subgroup in the group of all unitriangular matrices of dimension 3 over the field of rationals that is not computable but the sections of any of its central series are computable.
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Original Russian Text Copyright © 2014 Nurizinov M.K., Tyulyubergenev R.K, and Khisamiev N.G.
The authors were supported by the Ministry of Education and Science of the Republic of Kazakhstan (Grants 0726/GF and 0929/GFZ).
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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 55, No. 3, pp. 580–591, May–June, 2014.
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Nurizinov, M.K., Tyulyubergenev, R.K. & Khisamiev, N.G. Computable torsion-free nilpotent groups of finite dimension. Sib Math J 55, 471–481 (2014). https://doi.org/10.1134/S0037446614030094
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DOI: https://doi.org/10.1134/S0037446614030094