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∞.
Martínez-Pérez, C., Matucci, F., Nucinkis, B. (2016). Cohomological finiteness conditions and centralisers in generalisations of Thompson's group v. FORUM MATHEMATICUM, 28(5), 909-921 [10.1515/forum-2014-0176].
Cohomological finiteness conditions and centralisers in generalisations of Thompson's group v
Matucci, FrancescoCo-primo
;
2016
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∞.
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