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Algebra Logika, 2007, Volume 46, Number 1, Pages 46–59 (Mi al8)  

This article is cited in 17 scientific papers (total in 17 papers)

The property of being equationally Noetherian for some soluble groups

Ch. K. Guptaa, N. S. Romanovskiib

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

Abstract: Let $\mathfrak B$ be a class of groups $A$ which are soluble, equationally Noetherian, and have a central series
$$ A=A_1\geqslant A_2 \geqslant\ldots A_n\geqslant\ldots $$
such that $\bigcap A_n=1$ and all factors $A_n/A_{n+1}$ are torsion-free groups; $D$ is a direct product of finitely many cyclic groups of infinite or prime orders. We prove that the wreath product $D\wr A$ is an equationally Noetherian group. As a consequence we show that free soluble groups of arbitrary derived lengths and ranks are equationally Noetherian.

Keywords: equationally Noetherian group, free soluble group.

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English version:
Algebra and Logic, 2007, 46:1, 28–36

Bibliographic databases:

UDC: 512.5
Received: 30.05.2006

Citation: Ch. K. Gupta, N. S. Romanovskii, “The property of being equationally Noetherian for some soluble groups”, Algebra Logika, 46:1 (2007), 46–59; Algebra and Logic, 46:1 (2007), 28–36

Citation in format AMSBIB
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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. N. S. Romanovskii, I. P. Shestakov, “Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra”, Algebra and Logic, 47:4 (2008), 269–278  mathnet  crossref  mathscinet  zmath  isi
    2. N. S. Romanovskii, “Divisible rigid groups”, Algebra and Logic, 47:6 (2008), 426–434  mathnet  crossref  mathscinet  zmath  isi
    3. N. S. Romanovskii, “Equational Noetherianness of rigid soluble groups”, Algebra and Logic, 48:2 (2009), 147–160  mathnet  crossref  mathscinet  zmath  isi
    4. N. S. Romanovskii, “Irreducible algebraic sets over divisible decomposed rigid groups”, Algebra and Logic, 48:6 (2009), 449–464  mathnet  crossref  mathscinet  zmath  isi
    5. S. G. Melesheva, “Equations and algebraic geometry over profinite groups”, Algebra and Logic, 49:5 (2010), 444–455  mathnet  crossref  mathscinet  zmath  isi  elib
    6. Myasnikov A., Romanovskiy N., “Krull dimension of solvable groups”, J. Algebra, 324:10 (2010), 2814–2831  crossref  mathscinet  zmath  isi  elib  scopus
    7. N. S. Romanovskii, “Coproducts of rigid groups”, Algebra and Logic, 49:6 (2010), 539–550  mathnet  crossref  mathscinet  isi
    8. A. G. Myasnikov, N. S. Romanovskii, “Universal theories for rigid soluble groups”, Algebra and Logic, 50:6 (2012), 539–552  mathnet  crossref  mathscinet  zmath  isi
    9. 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
    10. Romanovskiy N.S., “Presentations for Rigid Solvable Groups”, J. Group Theory, 15:6 (2012), 793–810  crossref  mathscinet  zmath  isi  elib  scopus
    11. M. V. Kotov, “Topologizability of countable equationally Noetherian algebras”, Algebra and Logic, 52:2 (2013), 105–115  mathnet  crossref  mathscinet  isi
    12. V. A. Roman'kov, N. G. Khisamiev, “Verbally and existentially closed subgroups of free nilpotent groups”, Algebra and Logic, 52:4 (2013), 336–351  mathnet  crossref  mathscinet  isi
    13. N. S. Romanovskii, “Irreducibility of an affine space in algebraic geometry over a group”, Algebra and Logic, 52:3 (2013), 262–265  mathnet  crossref  mathscinet  isi
    14. Myasnikov A.G. Romanovskii N.S., “Logical Aspects of the Theory of Divisible Rigid Groups”, Dokl. Math., 90:3 (2014), 697–698  crossref  mathscinet  zmath  isi  elib  scopus
    15. A. G. Myasnikov, N. S. Romanovskii, “Model-theoretic aspects of the theory of divisible rigid soluble groups”, Algebra and Logic, 56:1 (2017), 82–84  mathnet  crossref  crossref  isi
    16. V. A. Roman'kov, “Solvability of equations in classes of solvable groups and Lie algebras”, Algebra and Logic, 56:3 (2017), 251–255  mathnet  crossref  crossref  mathscinet  isi
    17. N. S. Romanovskii, “Divisible rigid groups. Algebraic closedness and elementary theory”, Algebra and Logic, 56:5 (2017), 395–408  mathnet  crossref  crossref  isi
  • Алгебра и логика Algebra and Logic
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