Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V
Keyword(s):
Group V
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AbstractWe consider generalisations of Thompson’s group V, denoted by ${V_{r}(\Sigma)}$, which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, ${V_{r}(\Sigma)}$ is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type ${\operatorname{F}_{\infty}}$ and that this implies that also centralisers of finite subgroups are of type ${\operatorname{F}_{\infty}}$.
Keyword(s):
2012 ◽
Vol 154
(2)
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pp. 213-223
2016 ◽
Vol 93
(3)
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pp. 441-446
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Keyword(s):
2013 ◽
Vol 56
(7)
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pp. 1509-1520
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2016 ◽
Vol 52
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pp. 197-206
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2014 ◽
Vol 156
(2)
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pp. 343-361
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Keyword(s):
1997 ◽
Vol 10
(2)
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