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Sibirskii Matematicheskii Zhurnal, 2014, Volume 55, Number 3, Pages 580–591 (Mi smj2555)  
This article is cited in 2 scientific papers (total in 3 papers)

Computable torsion-free nilpotent groups of finite dimension

M. K. Nurizinov, R. K. Tyulyubergenev, N. G. Khisamiev

East Kazakhstan State Technical University, Ust'-Kamenogorsk, Kazakhstan
Full-text PDF (338 kB) Citations (3)
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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.
Keywords: dimension of a group, nilpotent torsion-free group of finite dimension, unitriangular matrix over the fields of rationals, central series, sections of the central series, computable group, principal computable enumeration.
Received: 30.10.2013
English version:
Siberian Mathematical Journal, 2014, Volume 55, Issue 3, Pages 471–481
DOI: https://doi.org/10.1134/S0037446614030094
Bibliographic databases:
Document Type: Article
UDC: 512.54+510.5
Language: Russian
Citation: M. K. Nurizinov, R. K. Tyulyubergenev, N. G. Khisamiev, “Computable torsion-free nilpotent groups of finite dimension”, Sibirsk. Mat. Zh., 55:3 (2014), 580–591; Siberian Math. J., 55:3 (2014), 471–481
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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