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Sibirskii Matematicheskii Zhurnal, 2012, Volume 53, Number 5, Pages 1133–1146 (Mi smj2335)  
This article is cited in 3 scientific papers (total in 3 papers)

On positive and constructive groups

N. G. Khisamiev

East Kazakhstan State Technical University named after D. Serikbayev, Ust-Kamenogorsk, Kazakhstan
Full-text PDF (339 kB) Citations (3)
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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.
Keywords: $R$-group, positive (constructive) group, positivizable (constructivizable) group, commutant, center of a group, dimension of a group, computably enumerable (computable) group.
Received: 09.06.2011
English version:
Siberian Mathematical Journal, 2012, Volume 53, Issue 5, Pages 906–917
DOI: https://doi.org/10.1134/S0037446612050151
Bibliographic databases:
Document Type: Article
UDC: 512.540+510.5
Language: Russian
Citation: N. G. Khisamiev, “On positive and constructive groups”, Sibirsk. Mat. Zh., 53:5 (2012), 1133–1146; Siberian Math. J., 53:5 (2012), 906–917
Citation in format AMSBIB
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\paper On positive and constructive groups
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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