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Sibirsk. Mat. Zh., 2018, Volume 59, Number 3, Pages 514–528 (Mi smj2990)  

This article is cited in 1 scientific paper (total in 1 paper)

On the centralizer dimension and lattice of generalized Baumslag–Solitar groups

F. A. Dudkinab

a Sobolev Institute of Mathematics, Novosibirsk, Russia
b Novosibirsk State University, Novosibirsk, Russia

Abstract: A generalized Baumslag–Solitar group (a $GBS$ group) is a finitely generated group $G$ acting on a tree so that all vertex and edge stabilizers are infinite cyclic groups. Each $GBS$ group is the fundamental group $\pi_1(\mathbb A)$ of some labeled graph $\mathbb A$. We describe the centralizers of elements and the centralizer lattice. Also, we find the centralizer dimension for $GBS$ groups if $\mathbb A$ is a labeled tree.

Keywords: centralizer lattice, centralizer dimension, generalized Baumslag–Solitar group.

Funding Agency Grant Number
Russian Science Foundation 14-21-00065
The work is supported by the Russian Science Foundation (project 14-21-00065).


DOI: https://doi.org/10.17377/smzh.2018.59.303

Full text: PDF file (377 kB)
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English version:
Siberian Mathematical Journal, 2018, 59:3, 403–414

Bibliographic databases:

UDC: 512.54
MSC: 35R30
Received: 27.04.2017

Citation: F. A. Dudkin, “On the centralizer dimension and lattice of generalized Baumslag–Solitar groups”, Sibirsk. Mat. Zh., 59:3 (2018), 514–528; Siberian Math. J., 59:3 (2018), 403–414

Citation in format AMSBIB
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\paper On the centralizer dimension and lattice of generalized Baumslag--Solitar groups
\jour Sibirsk. Mat. Zh.
\yr 2018
\vol 59
\issue 3
\pages 514--528
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\crossref{https://doi.org/10.17377/smzh.2018.59.303}
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\transl
\jour Siberian Math. J.
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\vol 59
\issue 3
\pages 403--414
\crossref{https://doi.org/10.1134/S0037446618030035}
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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. F. A. Dudkin, “Computation of the centralizer dimension of generalized Baumslag–Solitar groups”, Sib. elektron. matem. izv., 15 (2018), 1823–1841  mathnet  crossref
  • Сибирский математический журнал Siberian Mathematical Journal
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