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Algebra Logika, 2014, Volume 53, Number 1, Pages 45–59 (Mi al623)  

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

Existentially closed subgroups of free nilpotent groups

V. A. Roman'kovab, N. G. Khisamievc

a Dostoevskii Omsk State University, pr. Mira 55-A, Omsk, 644077, Russia
b Omsk State Technical University, pr. Mira 11, Omsk, 644050, Russia
c Serikbaev East Kazakhstan State Technical University, ul. Serikbaeva 19, Ust-Kamenogorsk, 070010, Kazakhstan

Abstract: Let $\mathcal N_c$ be a variety of all nilpotent groups of class at most $c$, and let $N_{r,c}$ be a free nilpotent group of finite rank $r$ and nilpotency class $c$. It is proved that a subgroup $N$ of $N_{r,c}$ for $c\ge3$ is existentially closed in $N_{r,c}$ iff $N$ is a free factor of the group $N_{r,c}$ with respect to the variety $\mathcal N_c$. Consequently, $N\simeq N_{m,c}$, $1\le m\le r$ and $m\ge c-1$.

Keywords: existentially closed subgroup, free nilpotent group, discriminating extension.

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English version:
Algebra and Logic, 2014, 53:1, 29–38

Bibliographic databases:

UDC: 512.54
Received: 23.06.2013
Revised: 04.11.2013

Citation: V. A. Roman'kov, N. G. Khisamiev, “Existentially closed subgroups of free nilpotent groups”, Algebra Logika, 53:1 (2014), 45–59; Algebra and Logic, 53:1 (2014), 29–38

Citation in format AMSBIB
\Bibitem{RomKhi14}
\by V.~A.~Roman'kov, N.~G.~Khisamiev
\paper Existentially closed subgroups of free nilpotent groups
\jour Algebra Logika
\yr 2014
\vol 53
\issue 1
\pages 45--59
\mathnet{http://mi.mathnet.ru/al623}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3237622}
\transl
\jour Algebra and Logic
\yr 2014
\vol 53
\issue 1
\pages 29--38
\crossref{https://doi.org/10.1007/s10469-014-9269-6}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000337279400004}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84902306093}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. V. A. Roman'kov, N. G. Khisamiev, A. A. Konyrkhanova, “Algebraically and verbally closed subgroups and retracts of finitely generated nilpotent groups”, Siberian Math. J., 58:3 (2017), 536–545  mathnet  crossref  crossref  isi  elib  elib
  • Алгебра и логика Algebra and Logic
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