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Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports], 2018, Volume 15, Pages 1823–1841
DOI: https://doi.org/10.33048/semi.2018.15.147 (Mi semr1038) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Mathematical logic, algebra and number theory

Computation of the centralizer dimension of generalized Baumslag–Solitar groups

F. A. Dudkinab

a Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
b Novosibirsk State University, Pirogova St., 2, 630090, Novosibirsk, Russia
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DOI: https://doi.org/10.33048/semi.2018.15.147
Abstract: A finitely generated group $G$ acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups is called a generalized Baumslag-Solitar group ($GBS$ group). The centralizer dimension of a group $G$ is the maximal length of a descending chain of centralizers. In this paper we complete a description of centralizers for unimodular $GBS$ groups. This allows us to find the centralizer dimension of all $GBS$ groups and to establish a way to compute it.
Keywords: centralizer of set of elements, centralizer dimension, generalized Baumslag–Solitar group, Baumslag–Solitar group.
Funding agency Grant number
Russian Science Foundation 14-21-00065
The work was supported by Russian Science Foundation (project 14-21-00065).
Received July 22, 2018, published December 30, 2018
Bibliographic databases:
Document Type: Article
UDC: 512.54
MSC: 20E06
Language: English
Citation: F. A. Dudkin, “Computation of the centralizer dimension of generalized Baumslag–Solitar groups”, Sib. Èlektron. Mat. Izv., 15 (2018), 1823–1841
Citation in format AMSBIB
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\by F.~A.~Dudkin
\paper Computation of the centralizer dimension of generalized Baumslag--Solitar groups
\jour Sib. \`Elektron. Mat. Izv.
\yr 2018
\vol 15
\pages 1823--1841
\mathnet{http://mi.mathnet.ru/semr1038}
\crossref{https://doi.org/10.33048/semi.2018.15.147}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000454860200087}
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    • This publication is cited in the following 5 articles:
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