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This article is cited in 2 scientific papers (total in 2 papers)
Properties and universal theories for partially commutative nilpotent metabelian groups
Ch. K. Guptaa, E. I. Timoshenkob a University of Manitoba, Winnipeg, Canada
b Novosibirsk State Technical University, Novosibirsk, Russia
Abstract:
Partially commutative nilpotent metabelian groups are considered. We describe how annihilators of elements of the commutator subgroup of a group $G$, as well as centralizers of elements of $G$ in its commutator subgroup $G'$, are structured. It turns out that in the case where a defining graph of a group is a tree, the intersection of centralizers of distinct vertices and $G'$ coincides with the last nontrivial commutator subgroup of $G$. Universal theories for partially commutative nilpotent metabelian groups are compared: conditions on defining graphs of two partially commutative nilpotent metabelian groups are formulated which are sufficient for the two groups to have equal universal theories; conditions on defining graphs of two partially commutative metabelian groups are specified which are sufficient for the two groups to be universally equivalent; a criterion is given that decides whether two partially commutative nilpotent metabelian groups defined by trees are universally equivalent.
Keywords:
partially commutative nilpotent metabelian groups, annihilator, centralizer, graph of group, tree, universal theory.
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English version:
Algebra and Logic, 2012, 51:4, 285–305
Bibliographic databases:
UDC:
512.5 Received: 01.11.2011 Revised: 12.07.2012
Citation:
Ch. K. Gupta, E. I. Timoshenko, “Properties and universal theories for partially commutative nilpotent metabelian groups”, Algebra Logika, 51:4 (2012), 429–457; Algebra and Logic, 51:4 (2012), 285–305
Citation in format AMSBIB
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http://mi.mathnet.ru/eng/al545 http://mi.mathnet.ru/eng/al/v51/i4/p429
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This publication is cited in the following articles:
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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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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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