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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2006, Volume 3, Pages 197–215
(Mi semr198)
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This article is cited in 20 scientific papers (total in 20 papers)
Research papers
Centraliser dimension and universal classes of groups
Andrew J. Duncana, Ilya V. Kazatchkovb, Vladimir N. Remeslennikovc a School of Mathematics and Statistics, University of Newcastle
b Department of Mathematics and Statistics, McGill University,
Montreal, Quebec
c Omsk Branch of Mathematical Institute SB RAS
Abstract:
In this paper we establish results that will be required for the study of the algebraic geometry of partially commutative groups. We define classes of groups axiomatized by sentences determined by a graph. Among the classes which arise this way we find $\mathrm{CSA}$ and $\mathrm{CT}$ groups. We study the centralisers of a group, with particular attention to the height of the lattice of centralisers, which we call the centraliser dimension of the group. The behaviour of centraliser dimension under several common group operations is described. Groups with centraliser dimension $2$ are studied in detail. It is shown that $\mathrm{CT}$-groups are precisely those with centraliser dimension $2$ and trivial centre.
Received November 14, 2005, published June 7, 2006
Citation:
Andrew J. Duncan, Ilya V. Kazatchkov, Vladimir N. Remeslennikov, “Centraliser dimension and universal classes of groups”, Sib. Èlektron. Mat. Izv., 3 (2006), 197–215
Linking options:
https://www.mathnet.ru/eng/semr198 https://www.mathnet.ru/eng/semr/v3/p197
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Abstract page: | 382 | Full-text PDF : | 113 | References: | 81 |
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