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

Conchita Martinez-Perez, Francesco Matucci, Brita Nucinkis

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Abstract

We consider generalisations of Thompson's group V, denoted by Vr(Σ), which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, Vr(Σ) is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type F∞ and that this implies that also centralisers of finite subgroups are of type F∞.
Original languageEnglish
Pages (from-to)909-921
Number of pages13
JournalForum Mathematicum
Volume28
Issue number5
Early online date20 Oct 2015
DOIs
Publication statusPublished - 1 Sep 2016

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