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Algebra i logika, 2022, Volume 61, Number 1, Pages 77–92
DOI: https://doi.org/10.33048/alglog.2022.61.104
(Mi al2697)
 

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

Levi classes of quasivarieties of nilpotent groups of exponent $p^s$

V. V. Lodeishchikovaa, S. A. Shakhovab

a Altai State University, Barnaul
b Altai State University, Barnaul
Full-text PDF (237 kB) Citations (1)
References:
Abstract: The Levi class $L(\mathcal{M})$ generated by the class $\mathcal{M}$ of groups is the class of all groups in which the normal closure of every element belongs to $\mathcal{M}$. It is proved that there exists a set of quasivarieties $\mathcal{M}$ of cardinality continuum such that $L(\mathcal{M})=L(qH_{p^{s}})$, where $qH_{p^{s}}$ is the quasivariety generated by the group $H_{p^{s}}$, a free group of rank $2$ in the variety $\mathcal{R}^{p^{s}}$ of $\leq 2$-step nilpotent groups of exponent $p^{s}$ with commutator subgroup of exponent $p$, $p$ is a prime number, $p\neq 2$, $s$ is a natural number, $s\geq 2$, and $s>2$ for $p=3$.
Keywords: quasivariety, Levi class, nilpotent group.
Received: 21.01.2022
Revised: 07.06.2022
Bibliographic databases:
Document Type: Article
UDC: 512.54.01
Language: Russian
Citation: V. V. Lodeishchikova, S. A. Shakhova, “Levi classes of quasivarieties of nilpotent groups of exponent $p^s$”, Algebra Logika, 61:1 (2022), 77–92
Citation in format AMSBIB
\Bibitem{LodSha22}
\by V.~V.~Lodeishchikova, S.~A.~Shakhova
\paper Levi classes of quasivarieties of nilpotent groups of exponent $p^s$
\jour Algebra Logika
\yr 2022
\vol 61
\issue 1
\pages 77--92
\mathnet{http://mi.mathnet.ru/al2697}
\crossref{https://doi.org/10.33048/alglog.2022.61.104}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4471695}
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  • https://www.mathnet.ru/eng/al/v61/i1/p77
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Алгебра и логика Algebra and Logic
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    Abstract page:112
    Full-text PDF :41
    References:31
    First page:3
     
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