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Algebra Logika, 2004, Volume 43, Number 3, Pages 341–352 (Mi al74)  

This article is cited in 9 scientific papers (total in 9 papers)

Metabelian Products of Groups

V. N. Remeslennikov, N. S. Romanovskiia

a Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We prove a number of facts on metabelian products of metabelian groups, useful in algebraic geometry over groups. Namely, for a metabelian product of arbitrary metabelian groups, we look at the structure of a derived subgroup, and the Fitting radical; find criteria determining when a metabelian product of $u$-groups is again a $u$-group; and specify conditions under which a metabelian product of metabelian groups is a strong semidomain.

Keywords: metabelian group, metabelian product, $u$-group, derived subgroup, Fitting radical, strong semidomain

Full text: PDF file (174 kB)
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English version:
Algebra and Logic, 2004, 43:3, 190–197

Bibliographic databases:

UDC: 512.5
Received: 03.03.2003

Citation: V. N. Remeslennikov, N. S. Romanovskii, “Metabelian Products of Groups”, Algebra Logika, 43:3 (2004), 341–352; Algebra and Logic, 43:3 (2004), 190–197

Citation in format AMSBIB
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\by V.~N.~Remeslennikov, N.~S.~Romanovskii
\paper Metabelian Products of Groups
\jour Algebra Logika
\yr 2004
\vol 43
\issue 3
\pages 341--352
\mathnet{http://mi.mathnet.ru/al74}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2084040}
\zmath{https://zbmath.org/?q=an:1058.20028}
\elib{https://elibrary.ru/item.asp?id=9127550}
\transl
\jour Algebra and Logic
\yr 2004
\vol 43
\issue 3
\pages 190--197
\crossref{https://doi.org/10.1023/B:ALLO.0000028932.26405.a9}
\elib{https://elibrary.ru/item.asp?id=14165448}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846605291}


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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. Amaglobeli M.G., Remeslennikov V.N., “G-free metabelian nilpotent groups”, Doklady Mathematics, 70:3 (2004), 884–886  mathscinet  isi
    2. V. N. Remeslennikov, N. S. Romanovskii, “Irreducible Algebraic Sets in Metabelian Groups”, Algebra and Logic, 44:5 (2005), 336–347  mathnet  crossref  mathscinet  zmath
    3. M. G. Amaglobeli, “Algebraic sets and coordinate groups for a free nilpotent group of nilpotency class 2”, Siberian Math. J., 48:1 (2007), 3–7  mathnet  crossref  mathscinet  zmath  isi
    4. Daniyarova E., Myasnikov A., Remeslennikov V., “Unification theorems in algebraic geometry”, Aspects of Infinite Groups, Algebra and Discrete Mathematics, 1, 2008, 80–111  mathscinet  zmath  isi
    5. N. S. Romanovskii, “Irreducible algebraic sets over divisible decomposed rigid groups”, Algebra and Logic, 48:6 (2009), 449–464  mathnet  crossref  mathscinet  zmath  isi
    6. Myasnikov A., Romanovskiy N., “Krull dimension of solvable groups”, Journal of Algebra, 324:10 (2010), 2814–2831  crossref  mathscinet  zmath  isi  scopus
    7. Ch. K. Gupta, E. I. Timoshenko, “Universal theories for partially commutative metabelian groups”, Algebra and Logic, 50:1 (2011), 1–16  mathnet  crossref  mathscinet  zmath  isi
    8. E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. II. Foundations”, J. Math. Sci., 185:3 (2012), 389–416  mathnet  crossref
    9. E. I. Timoshenko, “Quasivarieties generated by partially commutative groups”, Siberian Math. J., 54:4 (2013), 722–730  mathnet  crossref  mathscinet  isi
  • Алгебра и логика Algebra and Logic
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