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arXiv 1309.7858math.GR
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Thompson群V推广的上同调有限性条件和中心化子

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

Conchita Martinez-Perez, Francesco Matucci, Brita E. A. Nucinkis

备注：
19 pages, 2 figures. Revised version. The original submission has now been split into two papers. The current submission contains the first one. The second part is being reworked and will be reposted soon independently. Lemma 4.8 was incorrect as stated and has since been rectified. The results of the paper are unchanged
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摘要：

我们考虑推广汤普森的组$V$，表示为$V_r(Σ)$，其中还包括组Higman，斯坦和布林。在适当的假设下，证明了$V_r(Σ)$是Cantor-代数的全自同构群.在一些进一步的小的限制下，我们证明了这些群是$\mathrm{F}_\infty$型的，这意味着有限子群的中心化子也是$\mathrm{F}_\infty$型的。

英文摘要：

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

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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