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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2020, Volume 17, Pages 2131–2141
DOI: https://doi.org/10.33048/semi.2020.17.143
(Mi semr1337)
 

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

Mathematical logic, algebra and number theory

Quasivarieties of nilpotent groups of axiomatic rank $4$

A. I. Budkin

Altai State University, 61, Lenina ave., Barnaul, 656049, Russia
Full-text PDF (319 kB) Citations (2)
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Abstract: We say that the axiomatic rank of a quasivariety $K$ is equal to $n$ if $K$ can be defined by a system of quasi-identities in $n$ variables and cannot be defined by any set of quasi-identities in fewer variables. If there is no such $n$, then $K$ has an infinite axiomatic rank. We prove that the set of quasivarieties of nilpotent torsion-free groups of class at most $2$ of axiomatic rank $4$ is continual.
Keywords: nilpotent group, quasivariety, variety, axiomatic rank.
Received April 16, 2020, published December 22, 2020
Bibliographic databases:
Document Type: Article
UDC: 512.5
MSC: 20E10
Language: English
Citation: A. I. Budkin, “Quasivarieties of nilpotent groups of axiomatic rank $4$”, Sib. Èlektron. Mat. Izv., 17 (2020), 2131–2141
Citation in format AMSBIB
\Bibitem{Bud20}
\by A.~I.~Budkin
\paper Quasivarieties of nilpotent groups of axiomatic rank~$4$
\jour Sib. \`Elektron. Mat. Izv.
\yr 2020
\vol 17
\pages 2131--2141
\mathnet{http://mi.mathnet.ru/semr1337}
\crossref{https://doi.org/10.33048/semi.2020.17.143}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000610961200001}
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  • https://www.mathnet.ru/eng/semr/v17/p2131
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
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    Full-text PDF :68
    References:31
     
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