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Sibirsk. Mat. Zh., 2012, Volume 53, Number 5, Pages 1133–1146 (Mi smj2335)  

This article is cited in 2 scientific papers (total in 2 papers)

On positive and constructive groups

N. G. Khisamiev

East Kazakhstan State Technical University named after D. Serikbayev, Ust-Kamenogorsk, Kazakhstan

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.

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English version:
Siberian Mathematical Journal, 2012, 53:5, 906–917

Bibliographic databases:

UDC: 512.540+510.5
Received: 09.06.2011

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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\by N.~G.~Khisamiev
\paper On positive and constructive groups
\jour Sibirsk. Mat. Zh.
\yr 2012
\vol 53
\issue 5
\pages 1133--1146
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\elib{http://elibrary.ru/item.asp?id=17897071}
\transl
\jour Siberian Math. J.
\yr 2012
\vol 53
\issue 5
\pages 906--917
\crossref{https://doi.org/10.1134/S0037446612050151}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. K. Nurizinov, R. K. Tyulyubergenev, N. G. Khisamiev, “Computable torsion-free nilpotent groups of finite dimension”, Siberian Math. J., 55:3 (2014), 471–481  mathnet  crossref  mathscinet  isi  elib
    2. N. G. Khisamiev, I. V. Latkin, “On constructive nilpotent groups”, Computability and Complexity: Essays Dedicated to Rodney G. Downey on the Occasion of His 60Th Birthday, Lecture Notes in Computer Science, 10010, eds. A. Day, M. Fellows, N. Greenberg, B. Khoussainov, A. Melnikov, F. Rosamond, Springler, 2017, 324–353  crossref  mathscinet  zmath  isi  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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