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Algebra Logika, 2009, Volume 48, Number 3, Pages 309–341 (Mi al402)  

This article is cited in 19 scientific papers (total in 19 papers)

Partially commutative metabelian groups: centralizers and elementary equivalence

Ch. K. Guptaa, E. I. Timoshenkob

a Dep. Math., Univ. Manitoba, Winnipeg, CANADA
b Novosibirsk State University of Architecture and Civil Engineering, Novosibirsk, RUSSIA

Abstract: For partially commutative metabelian groups, annihilators of elements of commutator subgroups are described; canonical representations of elements are defined; approximability by torsion-free nilpotent groups is proved; centralizers of elements are described. Also, it is proved that two partially commutative metabelian groups have equal elementary theories iff their defining graphs are isomorphic, and that every partially commutative metabelian group is embeddable in a metabelian group with decidable universal theory.

Keywords: metabelian group, centralizer, annihilator, elementary equivalence.

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English version:
Algebra and Logic, 2009, 48:3, 173–192

Bibliographic databases:

UDC: 512.5
Received: 07.04.2008

Citation: Ch. K. Gupta, E. I. Timoshenko, “Partially commutative metabelian groups: centralizers and elementary equivalence”, Algebra Logika, 48:3 (2009), 309–341; Algebra and Logic, 48:3 (2009), 173–192

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. E. I. Timoshenko, “Universal equivalence of partially commutative metabelian groups”, Algebra and Logic, 49:2 (2010), 177–196  mathnet  crossref  mathscinet  zmath  isi
    2. 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
    3. E. N. Poroshenko, “Bases for partially commutative Lie algebras”, Algebra and Logic, 50:5 (2011), 405–417  mathnet  crossref  mathscinet  zmath  isi
    4. 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
    5. M. Casals-Ruiz, I. V. Kazachkov, “Two remarks on the first-order theories of Baumslag–Solitar groups”, Siberian Math. J., 53:5 (2012), 805–809  mathnet  crossref  mathscinet  isi  elib  elib
    6. Ch. K. Gupta, E. I. Timoshenko, “Properties and universal theories for partially commutative nilpotent metabelian groups”, Algebra and Logic, 51:4 (2012), 285–305  mathnet  crossref  mathscinet  zmath  isi
    7. E. N. Poroshenko, “Centralizers in partially commutative Lie algebras”, Algebra and Logic, 51:4 (2012), 351–371  mathnet  crossref  mathscinet  zmath  isi
    8. Poroshenko E.N., Timoshenko E.I., “Universal Equivalence of Partially Commutative Metabelian Lie Algebras”, J. Algebra, 384 (2013), 143–168  crossref  mathscinet  zmath  isi  elib  scopus
    9. E. I. Timoshenko, “Quasivarieties generated by partially commutative groups”, Siberian Math. J., 54:4 (2013), 722–730  mathnet  crossref  mathscinet  isi
    10. E. I. Timoshenko, “On a Presentation of the Automorphism Group of a Partially Commutative Metabelian Group”, Math. Notes, 97:2 (2015), 275–283  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    11. Poroshenko E.N., “on Universal Equivalence of Partially Commutative Metabelian Lie Algebras”, Commun. Algebr., 43:2 (2015), 746–762  crossref  mathscinet  zmath  isi  elib  scopus
    12. E. N. Poroshenko, “Universal equivalence of partially commutative Lie algebras”, Algebra and Logic, 56:2 (2017), 133–148  mathnet  crossref  crossref  isi
    13. E. I. Timoshenko, “Centralizer dimensions and universal theories for partially commutative metabelian groups”, Algebra and Logic, 56:2 (2017), 149–170  mathnet  crossref  crossref  isi
    14. E. N. Poroshenko, “Elementary equivalence of partially commutative Lie rings and algebras”, Algebra and Logic, 56:4 (2017), 348–352  mathnet  crossref  crossref  mathscinet  isi
    15. E. N. Poroshenko, “Universal equivalence of some countably generated partially commutative structures”, Siberian Math. J., 58:2 (2017), 296–304  mathnet  crossref  crossref  isi  elib  elib
    16. V. Ya. Bloshchitsyn, E. I. Timoshenko, “Comparison between the universal theories of partially commutative metabelian groups”, Siberian Math. J., 58:3 (2017), 382–391  mathnet  crossref  crossref  isi  elib  elib
    17. Timoshenko E., “On Embedding of Partially Commutative Metabelian Groups to Matrix Groups”, Int. J. Group Theory, 7:4 (2018), 17–26  crossref  mathscinet  isi  scopus
    18. E. I. Timoshenko, “Centralizer dimensions of partially commutative metabelian groups”, Algebra and Logic, 57:1 (2018), 69–80  mathnet  crossref  crossref  isi
    19. E. I. Timoshenko, “On splittings, subgroups, and theories of partially commutative metabelian groups”, Siberian Math. J., 59:3 (2018), 536–541  mathnet  crossref  crossref  isi  elib
  • Алгебра и логика Algebra and Logic
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