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Sibirsk. Mat. Zh., 2010, Volume 51, Number 6, Pages 1359–1366 (Mi smj2166)  

This article is cited in 3 scientific papers (total in 3 papers)

The Levi classes generated by nilpotent groups

V. V. Lodeyshchikova

Altai State University, Barnaul

Abstract: Given an arbitrary class $M$ of groups, denote by $L(M)$ the class of all groups $G$ in which the normal closure of every element belongs to $M$. Consider the quasivariety $qF_p$ generated by the relatively free group in the class of nilpotent groups of length at most 2 with the commutant of exponent $p$ (where $p$ is an odd prime). We describe the Levi class that is generated by $qF_p$.

Keywords: quasivariety, Levi class, nilpotent group.

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English version:
Siberian Mathematical Journal, 2010, 51:6, 1075–1080

Bibliographic databases:

UDC: 512.54.01
Received: 03.06.2009

Citation: V. V. Lodeyshchikova, “The Levi classes generated by nilpotent groups”, Sibirsk. Mat. Zh., 51:6 (2010), 1359–1366; Siberian Math. J., 51:6 (2010), 1075–1080

Citation in format AMSBIB
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\paper The Levi classes generated by nilpotent groups
\jour Sibirsk. Mat. Zh.
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\pages 1359--1366
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\issue 6
\pages 1075--1080
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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. S. A. Shakhova, “The axiomatic rank of Levi classes”, Algebra and Logic, 57:5 (2018), 381–391  mathnet  crossref  crossref  isi
    2. V. V. Lodeischikova, “O klasse Levi, porozhdennom kvazimnogoobraziem nilpotentnykh grupp”, Algebra i logika, 58:4 (2019), 486–499  mathnet  crossref
    3. A. I. Budkin, “The operator $L_n$ on quasivarieties of universal algebras”, Siberian Math. J., 60:4 (2019), 565–571  mathnet  crossref  crossref  isi  elib
  • Сибирский математический журнал Siberian Mathematical Journal
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