编织Higman-Thompson群近亲的有限性质

IF 0.6 3区数学 Q3 MATHEMATICS

Groups Geometry and Dynamics Pub Date : 2021-03-24 DOI:10.4171/ggd/731

Rachel Skipper, Xiaolei Wu

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引用次数: 5

摘要

我们研究了标签为$H\leq B_d$的编结Higman—Thompson群$bV_{d,r}(H)$和标签为$H\leq PB_d$的编结Higman—Thompson群$bF_{d,r}(H)$和$bT_{d,r}(H)$的有限性质，其中$B_d$是包含$d$字符串的编结群，$PB_d$是它的纯编结子群。我们表明，对于所有$d\geq 2$和$r\geq 1$，组$bV_{d,r}(H)$(参见:$bT_{d,r}(H)$或$bF_{d,r}(H)$)的类型为$F_n$，当且仅当$H$为。我们的结果尤其证实了阿罗卡和康普里多最近的一个猜想。

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Finiteness properties for relatives of braided Higman–Thompson groups

We study the finiteness properties of the braided Higman--Thompson group $bV_{d,r}(H)$ with labels in $H\leq B_d$, and $bF_{d,r}(H)$ and $bT_{d,r}(H)$ with labels in $H\leq PB_d$ where $B_d$ is the braid group with $d$ strings and $PB_d$ is its pure braid subgroup. We show that for all $d\geq 2$ and $r\geq 1$, the group $bV_{d,r}(H)$ (resp. $bT_{d,r}(H)$ or $bF_{d,r}(H)$) is of type $F_n$ if and only if $H$ is. Our result in particular confirms a recent conjecture of Aroca and Cumplido.

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来源期刊

Groups Geometry and Dynamics 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Groups, Geometry, and Dynamics is devoted to publication of research articles that focus on groups or group actions as well as articles in other areas of mathematics in which groups or group actions are used as a main tool. The journal covers all topics of modern group theory with preference given to geometric, asymptotic and combinatorial group theory, dynamics of group actions, probabilistic and analytical methods, interaction with ergodic theory and operator algebras, and other related fields. Topics covered include: geometric group theory; asymptotic group theory; combinatorial group theory; probabilities on groups; computational aspects and complexity; harmonic and functional analysis on groups, free probability; ergodic theory of group actions; cohomology of groups and exotic cohomologies; groups and low-dimensional topology; group actions on trees, buildings, rooted trees.