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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
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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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This publication is cited in the following articles:
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E. I. Timoshenko, “Universal equivalence of partially commutative metabelian groups”, Algebra and Logic, 49:2 (2010), 177–196
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Ch. K. Gupta, E. I. Timoshenko, “Universal theories for partially commutative metabelian groups”, Algebra and Logic, 50:1 (2011), 1–16
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E. N. Poroshenko, “Bases for partially commutative Lie algebras”, Algebra and Logic, 50:5 (2011), 405–417
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E. Yu. Daniyarova, A. G. Myasnikov, V. N. Remeslennikov, “Algebraic geometry over algebraic structures. II. Foundations”, J. Math. Sci., 185:3 (2012), 389–416
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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
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Ch. K. Gupta, E. I. Timoshenko, “Properties and universal theories for partially commutative nilpotent metabelian groups”, Algebra and Logic, 51:4 (2012), 285–305
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E. N. Poroshenko, “Centralizers in partially commutative Lie algebras”, Algebra and Logic, 51:4 (2012), 351–371
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Poroshenko E.N., Timoshenko E.I., “Universal Equivalence of Partially Commutative Metabelian Lie Algebras”, J. Algebra, 384 (2013), 143–168
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E. I. Timoshenko, “Quasivarieties generated by partially commutative groups”, Siberian Math. J., 54:4 (2013), 722–730
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E. I. Timoshenko, “On a Presentation of the Automorphism Group of a Partially Commutative Metabelian Group”, Math. Notes, 97:2 (2015), 275–283
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Poroshenko E.N., “on Universal Equivalence of Partially Commutative Metabelian Lie Algebras”, Commun. Algebr., 43:2 (2015), 746–762
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E. N. Poroshenko, “Universal equivalence of partially commutative Lie algebras”, Algebra and Logic, 56:2 (2017), 133–148
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E. I. Timoshenko, “Centralizer dimensions and universal theories for partially commutative metabelian groups”, Algebra and Logic, 56:2 (2017), 149–170
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E. N. Poroshenko, “Elementary equivalence of partially commutative Lie rings and algebras”, Algebra and Logic, 56:4 (2017), 348–352
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E. N. Poroshenko, “Universal equivalence of some countably generated partially commutative structures”, Siberian Math. J., 58:2 (2017), 296–304
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V. Ya. Bloshchitsyn, E. I. Timoshenko, “Comparison between the universal theories of partially commutative metabelian groups”, Siberian Math. J., 58:3 (2017), 382–391
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Timoshenko E., “On Embedding of Partially Commutative Metabelian Groups to Matrix Groups”, Int. J. Group Theory, 7:4 (2018), 17–26
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E. I. Timoshenko, “Centralizer dimensions of partially commutative metabelian groups”, Algebra and Logic, 57:1 (2018), 69–80
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E. I. Timoshenko, “On splittings, subgroups, and theories of partially commutative metabelian groups”, Siberian Math. J., 59:3 (2018), 536–541
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