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Sibirskii Matematicheskii Zhurnal, 2017, Volume 58, Number 1, Pages 56–63
DOI: https://doi.org/10.17377/smzh.2017.58.106 (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
Full-text PDF (284 kB) Citations (2)
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DOI: https://doi.org/10.17377/smzh.2017.58.106
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.
Received: 02.03.2016
English version:
Siberian Mathematical Journal, 2017, Volume 58, Issue 1, Pages 43–48
DOI: https://doi.org/10.1134/S0037446617010062
Bibliographic databases:
Document Type: Article
UDC: 512.57
Language: Russian
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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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Сибирский математический журнал Siberian Mathematical Journal
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