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# Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna

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CiteScore 2018: 0.71

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1435-5337
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Volume 28, Issue 5

# Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V

Conchita Martínez-Pérez
/ Francesco Matucci
• Département de Mathématiques, Bâtiment 425, Faculté des Sciences d’Orsay, Université Paris-Sud 11, 91405 Orsay Cedex, France
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• Other articles by this author:
/ Brita E. A. Nucinkis
• Corresponding author
• Department of Mathematics, Royal Holloway, University of London, Egham, Surrey TW20 0EX, United Kingdom of Great Britain and Northern Ireland
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• Other articles by this author:
Published Online: 2015-10-20 | DOI: https://doi.org/10.1515/forum-2014-0176

## Abstract

We consider generalisations of Thompson’s group V, denoted by ${V}_{r}\left(\mathrm{\Sigma }\right)$, which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, ${V}_{r}\left(\mathrm{\Sigma }\right)$ is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type ${F}_{\mathrm{\infty }}$ and that this implies that also centralisers of finite subgroups are of type ${F}_{\mathrm{\infty }}$.

MSC 2010: 20J05

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Revised: 2015-02-03

Published Online: 2015-10-20

Published in Print: 2016-09-01

This work was partially funded by an LMS Scheme 4 Grant 41209. The first named author was supported by Gobierno de Aragón, European Regional Development Funds and MTM2010-19938-C03-03. The second author gratefully acknowledges the Fondation Mathématique Jacques Hadamard (ANR-10-CAMP-0151-02 – FMJH – Investissement d’Avenir) for the support received during the development of this work.

Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 909–921, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741,

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## Citing Articles

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[2]
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[3]
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Bulletin of the London Mathematical Society, 2018