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Sibirsk. Mat. Zh., 2017, Volume 58, Number 1, Pages 56–63 (Mi smj2839)  

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

On quasivarieties of axiomatic rank $3$ of torsion-free nilpotent groups

A. I. Budkin

Altai State University, Barnaul, Russia

Abstract: We study the lattice of quasivarieties of axiomatic rank at most $3$ of torsion-free nilpotent groups of class at most $3$. We prove that this lattice has cardinality of the continuum and includes a sublattice that is order isomorphic to the set of real numbers. Also we establish that the lattice of quasivarieties of axiomatic rank at most $2$ of these groups is a $5$-element chain.

Keywords: nilpotent group, axiomatic rank, quasivarieties, lattice.

DOI: https://doi.org/10.17377/smzh.2017.58.106

Full text: PDF file (284 kB)
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English version:
Siberian Mathematical Journal, 2017, 58:1, 43–48

Bibliographic databases:

UDC: 512.57
Received: 02.03.2016

Citation: A. I. Budkin, “On quasivarieties of axiomatic rank $3$ of torsion-free nilpotent groups”, Sibirsk. Mat. Zh., 58:1 (2017), 56–63; Siberian Math. J., 58:1 (2017), 43–48

Citation in format AMSBIB
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\by A.~I.~Budkin
\paper On quasivarieties of axiomatic rank~$3$ of torsion-free nilpotent groups
\jour Sibirsk. Mat. Zh.
\yr 2017
\vol 58
\issue 1
\pages 56--63
\mathnet{http://mi.mathnet.ru/smj2839}
\crossref{https://doi.org/10.17377/smzh.2017.58.106}
\elib{http://elibrary.ru/item.asp?id=29159902}
\transl
\jour Siberian Math. J.
\yr 2017
\vol 58
\issue 1
\pages 43--48
\crossref{https://doi.org/10.1134/S0037446617010062}
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\elib{http://elibrary.ru/item.asp?id=29488042}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85014657875}


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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. A. I. Budkin, “On $2$-closedness of the rational numbers in quasivarieties of nilpotent groups”, Siberian Math. J., 58:6 (2017), 971–982  mathnet  crossref  crossref  isi  elib
    2. A. I. Budkin, “On dominions of the rationals in nilpotent groups”, Siberian Math. J., 59:4 (2018), 598–609  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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