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- W2964288013 abstract "Abstract We consider generalisations of Thompson’s group V , denoted by <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>V</m:mi> <m:mi>r</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>Σ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> ${V_{r}(Sigma)}$ , which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mrow> <m:msub> <m:mi>V</m:mi> <m:mi>r</m:mi> </m:msub> <m:mo></m:mo> <m:mrow> <m:mo>(</m:mo> <m:mi>Σ</m:mi> <m:mo>)</m:mo> </m:mrow> </m:mrow> </m:math> ${V_{r}(Sigma)}$ is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mo>F</m:mo> <m:mi>∞</m:mi> </m:msub> </m:math> ${operatorname{F}_{infty}}$ and that this implies that also centralisers of finite subgroups are of type <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msub> <m:mo>F</m:mo> <m:mi>∞</m:mi> </m:msub> </m:math> ${operatorname{F}_{infty}}$ ." @default.
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- W2964288013 date "2015-10-20" @default.
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- W2964288013 title "Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V" @default.
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- W2964288013 doi "https://doi.org/10.1515/forum-2014-0176" @default.
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