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Mat. Zametki, 1997, Volume 61, Issue 6, Pages 884–889 (Mi mz1572)  

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

Primitive elements of the free groups of the varieties $\mathfrak A\mathfrak N_n$

E. I. Timoshenko

Novosibirsk Engineering Building Institute

Abstract: For groups of the form $F/N'$, we find necessary and sufficient conditions for an element $g\in N/N'$ to belong to the normal closure of an element $h\in F/N'$. It is proved that, in contrast to the case of a free metabelian group, for a free group of the variety $\mathfrak A\mathfrak N_2$, there exists an element $h$ whose normal closure contains a primitive element $g$, but the elements $h$ and $g^{\pm1}$ are not conjugate. In the group $F(\mathfrak A\mathfrak N_2)$, two nonconjugate elements are chosen that have equal normal closures.

DOI: https://doi.org/10.4213/mzm1572

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English version:
Mathematical Notes, 1997, 61:6, 739–743

Bibliographic databases:

UDC: 512.54
Received: 19.12.1995

Citation: E. I. Timoshenko, “Primitive elements of the free groups of the varieties $\mathfrak A\mathfrak N_n$”, Mat. Zametki, 61:6 (1997), 884–889; Math. Notes, 61:6 (1997), 739–743

Citation in format AMSBIB
\Bibitem{Tim97}
\by E.~I.~Timoshenko
\paper Primitive elements of the free groups of the varieties $\mathfrak A\mathfrak N_n$
\jour Mat. Zametki
\yr 1997
\vol 61
\issue 6
\pages 884--889
\mathnet{http://mi.mathnet.ru/mz1572}
\crossref{https://doi.org/10.4213/mzm1572}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1629813}
\zmath{https://zbmath.org/?q=an:0920.20023}
\transl
\jour Math. Notes
\yr 1997
\vol 61
\issue 6
\pages 739--743
\crossref{https://doi.org/10.1007/BF02361216}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1997YE52200028}


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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. E. I. Timoshenko, “Center of some solvable groups with one defining relation”, Math. Notes, 64:6 (1998), 798–803  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. Timoshenko, EI, “Test elements and test rank of a free metabelian group”, Siberian Mathematical Journal, 41:6 (2000), 1200  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus
    3. Ekici N., Esmerligil Z., Ersalan D., “Ideals and primitive elements of some relatively free Lie algebras”, SpringerPlus, 5 (2016), 833  crossref  isi  elib  scopus
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