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Algebra Logika, 2012, Volume 51, Number 4, Pages 429–457 (Mi al545)  

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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\by Ch.~K.~Gupta, E.~I.~Timoshenko
\paper Properties and universal theories for partially commutative nilpotent metabelian groups
\jour Algebra Logika
\yr 2012
\vol 51
\issue 4
\pages 429--457
\mathnet{http://mi.mathnet.ru/al545}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3051816}
\zmath{https://zbmath.org/?q=an:06138179}
\transl
\jour Algebra and Logic
\yr 2012
\vol 51
\issue 4
\pages 285--305
\crossref{https://doi.org/10.1007/s10469-012-9192-7}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871360016}


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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. 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
    2. 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
  • Алгебра и логика Algebra and Logic
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