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Sibirsk. Mat. Zh., 2007, Volume 48, Number 1, Pages 214–223 (Mi smj18)  

This article is cited in 5 scientific papers (total in 5 papers)

On constructive nilpotent groups

N. G. Khisamiev

East Kazakhstan State Technical University named after D. Serikbayev

Abstract: We prove the following: (1) a torsion-free class 2 nilpotent group is constructivizable if and only if it is isomorphic to the extension of some constructive abelian group included in the center of the group by some constructive torsion-free abelian group and some recursive system of factors; (2) a constructivizable torsion-free class 2 nilpotent group whose commutant has finite rank is orderably constructivizable.

Keywords: constructive group, nilpotent group, computable subgroup, center, system of factors.

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English version:
Siberian Mathematical Journal, 2007, 48:1, 172–179

Bibliographic databases:

UDC: 512.54+510.5
Received: 28.06.2005
Revised: 29.05.2006

Citation: N. G. Khisamiev, “On constructive nilpotent groups”, Sibirsk. Mat. Zh., 48:1 (2007), 214–223; Siberian Math. J., 48:1 (2007), 172–179

Citation in format AMSBIB
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\by N.~G.~Khisamiev
\paper On constructive nilpotent groups
\jour Sibirsk. Mat. Zh.
\yr 2007
\vol 48
\issue 1
\pages 214--223
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2304890}
\zmath{https://zbmath.org/?q=an:1154.20034}
\transl
\jour Siberian Math. J.
\yr 2007
\vol 48
\issue 1
\pages 172--179
\crossref{https://doi.org/10.1007/s11202-007-0018-0}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846626783}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. G. Khisamiev, “Torsion-free constructive nilpotent $R_p$-groups”, Siberian Math. J., 50:1 (2009), 181–187  mathnet  crossref  mathscinet  isi
    2. N. G. Khisamiev, “On positive and constructive groups”, Siberian Math. J., 53:5 (2012), 906–917  mathnet  crossref  mathscinet  isi  elib
    3. 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
    4. Melnikov A.G., “Computable Abelian Groups”, Bull. Symb. Log., 20:3 (2014), 315–356  crossref  mathscinet  zmath  isi  elib  scopus
    5. Conidis Ch.J., Shore R.A., “the Complexity of Ascendant Sequences in Locally Nilpotent Groups”, Int. J. Algebr. Comput., 24:2 (2014), 189–205  crossref  mathscinet  zmath  isi  elib  scopus
  • Сибирский математический журнал Siberian Mathematical Journal
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