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Sib. Èlektron. Mat. Izv., 2008, Volume 5, Pages 151–176 (Mi semr96)  

This article is cited in 5 scientific papers (total in 5 papers)

Research papers

Orthogonal systems in finite graphs

A. J. Duncana, I. V. Kazachkovb, V. N. Remeslennikovc

a School of Mathematics and Statistics, University of Newcastle, Newcastle upon Tyne
b Department of Mathematics and Statistics, McGill University
c Omsk Branch of Mathematical Institute SB RAS

Abstract: To a finite graph there corresponds a free partially commutative group: with the given graph as commutation graph. In this paper we construct an orthogonality theory for graphs and their corresponding free partially commutative groups. The theory developed here provides tools for the study of the structure of partially commutative groups, their universal theory and automorphism groups. In particular the theory is applied in this paper to the centraliser lattice of such groups.

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Document Type: Article
UDC: 512.54, 519.17
MSC: 05C25, 20E15
Received March 1, 2008, published March 31, 2008
Language: English

Citation: A. J. Duncan, I. V. Kazachkov, V. N. Remeslennikov, “Orthogonal systems in finite graphs”, Sib. Èlektron. Mat. Izv., 5 (2008), 151–176

Citation in format AMSBIB
\Bibitem{DunKazRem08}
\by A.~J.~Duncan, I.~V.~Kazachkov, V.~N.~Remeslennikov
\paper Orthogonal systems in finite graphs
\jour Sib. \`Elektron. Mat. Izv.
\yr 2008
\vol 5
\pages 151--176
\mathnet{http://mi.mathnet.ru/semr96}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2586627}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ch. K. Gupta, E. I. Timoshenko, “Partially commutative metabelian groups: centralizers and elementary equivalence”, Algebra and Logic, 48:3 (2009), 173–192  mathnet  crossref  mathscinet  zmath  isi
    2. V. N. Remeslennikov, A. V. Treier, “Structure of the automorphism group for partially commutative class two nilpotent groups”, Algebra and Logic, 49:1 (2010), 43–67  mathnet  crossref  mathscinet  zmath  isi
    3. Duncan A.J., Kazachkov I.V., Remeslennikov V.N., “Automorphisms of partially commutative groups I: Linear subgroups”, Groups Geom. Dyn., 4:4 (2010), 739–757  crossref  mathscinet  zmath  isi  elib
    4. 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
    5. Duncan A.J., Remeslennikov V.N., “Automorphisms of Partially Commutative Groups II: Combinatorial Subgroups”, Int. J. Algebr. Comput., 22:7 (2012), 1250074  crossref  mathscinet  mathscinet  zmath  isi  elib
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