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Sibirsk. Mat. Zh., 2013, Volume 54, Number 4, Pages 902–913 (Mi smj2465)  

This article is cited in 1 scientific paper (total in 1 paper)

Quasivarieties generated by partially commutative groups

E. I. Timoshenko

Novosibirsk State Technical University, Novosibirsk, Russia

Abstract: We prove that a partially commutative metabelian group is a subgroup in a direct product of torsion-free abelian groups and metabelian products of torsion-free abelian groups. From this we deduce that all partially commutative metabelian (nonabelian) groups generate the same quasivariety and prevariety. On the contrary, there exists an infinite chain of different quasivarieties generated by partially commutative groups with defining graphs of diameter 2.

Keywords: quasivariety, prevariety, partially commutative group, metabelian group, graph.

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English version:
Siberian Mathematical Journal, 2013, 54:4, 722–730

Bibliographic databases:

UDC: 512.5
Received: 03.07.2012

Citation: E. I. Timoshenko, “Quasivarieties generated by partially commutative groups”, Sibirsk. Mat. Zh., 54:4 (2013), 902–913; Siberian Math. J., 54:4 (2013), 722–730

Citation in format AMSBIB
\Bibitem{Tim13}
\by E.~I.~Timoshenko
\paper Quasivarieties generated by partially commutative groups
\jour Sibirsk. Mat. Zh.
\yr 2013
\vol 54
\issue 4
\pages 902--913
\mathnet{http://mi.mathnet.ru/smj2465}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3137155}
\transl
\jour Siberian Math. J.
\yr 2013
\vol 54
\issue 4
\pages 722--730
\crossref{https://doi.org/10.1134/S0037446613040125}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000323742800012}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84883311956}


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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. E. I. Timoshenko, “On splittings, subgroups, and theories of partially commutative metabelian groups”, Siberian Math. J., 59:3 (2018), 536–541  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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