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This article is cited in 15 scientific papers (total in 15 papers)
Universal theories for partially commutative metabelian groups
Ch. K. Guptaa, E. I. Timoshenkob
a University of Manitoba, Winnipeg, Canada
b Novosibirsk State Technical University, Novosibirsk, Russia
Abstract:
We look at properties of partially commutative metabelian groups and of their universal theories. In particular, it is shown that two partially commutative metabelian groups defined by cycles are universally equivalent if and only if the cycles are isomorphic.
Keywords:
partially commutative metabelian group, universal theory.
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English version:
Algebra and Logic, 2011, 50:1, 1–16
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UDC:
512.5
Received: 21.02.2010
Citation:
Ch. K. Gupta, E. I. Timoshenko, “Universal theories for partially commutative metabelian groups”, Algebra Logika, 50:1 (2011), 3–25; Algebra and Logic, 50:1 (2011), 1–16
Citation in format AMSBIB
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Citing articles on Google Scholar:
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Russian articles,
English articles
This publication is cited in the following articles:
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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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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, “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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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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E. N. Poroshenko, “Ob universalnoi ekvivalentnosti chastichno kommutativnykh algebr Li, opredelennykh grafami bez treugolnikov i kvadratov i bez izolirovannykh vershin”, Sib. elektron. matem. izv., 17 (2020), 933–953
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E. I. Timoshenko, “A basis for a partially commutative metabelian group”, Izv. Math., 85:4 (2021), 813–822
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E. N. Poroshenko, E. I. Timoshenko, “Partially commutative groups and Lie algebras”, Sib. elektron. matem. izv., 18:1 (2021), 668–693
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V. A. Roman'kov, “Algorithmic theory of solvable groups”, PDM, 2021, no. 52, 16–64
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