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Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia, 2020, Volume 490, Pages 5–8
DOI: https://doi.org/10.31857/S2686954320010105 (Mi danma22) 		 
This article is cited in 1 scientific paper (total in 1 paper)

MATHEMATICS

Varieties of exponential $MR$-groups

M. G. Amaglobeli

Ivane Javakhishvili Tbilisi State University, Tbilisi, Georgia
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DOI: https://doi.org/10.31857/S2686954320010105
Abstract: In this paper we introduce the notion of a variety of exponential $MR$-groups and tensor completions of groups in varieties. We study relationships between free groups of a given variety under different rings of scalars and describe varieties of abelian $MR$-groups. Moreover, in the category of $MR$-groups, we consider several analogs of $n$-class nilpotent groups. We got that the completion of a 2-class nilpotent group is a 2-class nilpotent.
Keywords: Lyndon $R$-groups, $MR$-groups, variety of $MR$-groups, $\alpha$-commutator, $R$-commutant, tensor completion, nilpotent $MR$-group.
Presented: Yu. L. Ershov
Received: 27.09.2019
Revised: 27.09.2019
Accepted: 31.10.2019
English version:
Doklady Mathematics, 2020, Volume 101, Issue 1, Pages 1–4
DOI: https://doi.org/10.1134/S106456242001010X
Bibliographic databases:
Document Type: Article
UDC: 512.544.33
Language: Russian
Citation: M. G. Amaglobeli, “Varieties of exponential $MR$-groups”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020), 5–8; Dokl. Math., 101:1 (2020), 1–4
Citation in format AMSBIB
\Bibitem{Ama20}
\by M.~G.~Amaglobeli
\paper Varieties of exponential $MR$-groups
\jour Dokl. RAN. Math. Inf. Proc. Upr.
\yr 2020
\vol 490
\pages 5--8
\mathnet{http://mi.mathnet.ru/danma22}
\crossref{https://doi.org/10.31857/S2686954320010105}
\zmath{https://zbmath.org/?q=an:1476.20067}
\transl
\jour Dokl. Math.
\yr 2020
\vol 101
\issue 1
\pages 1--4
\crossref{https://doi.org/10.1134/S106456242001010X}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85085008458}
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    • This publication is cited in the following 1 articles:
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    		Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia Doklady Rossijskoj Akademii Nauk. Mathematika, Informatika, Processy Upravlenia
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