论文标题
本地定义组的有限属性
Finiteness Properties of Locally Defined Groups
论文作者
论文摘要
让$ x $成为一套，让$ s $为$ x $的部分两种肉眼的反向半群。因此，$ s $的元素是两个$ x $的两个子集之间的两次射击，并且在取代函数和函数组成的操作下，需要关闭集合$ s $。我们将$γ_{s} $定义为$ x $的一组$ x $的自我投影集，其中每个$γ\inγ_{s} $中的每个$γ\都是有限的$ s $成员的结合。该集合是关于组成的组。 组$γ_{s} $组成一个包含大量研究的组的类，例如汤普森的$ v $，nekrashevych-röver群，霍顿的群组和Brin-Thompson Groups $ NV $等等。 我们为$γ_{s} $的几何模型提供了统一的结构，以及研究这些组的有限属性的一般框架。
Let $X$ be a set and let $S$ be an inverse semigroup of partial bijections of $X$. Thus, an element of $S$ is a bijection between two subsets of $X$, and the set $S$ is required to be closed under the operations of taking inverses and compositions of functions. We define $Γ_{S}$ to be the set of self-bijections of $X$ in which each $γ\in Γ_{S}$ is expressible as a union of finitely many members of $S$. This set is a group with respect to composition. The groups $Γ_{S}$ form a class containing numerous widely studied groups, such as Thompson's group $V$, the Nekrashevych-Röver groups, Houghton's groups, and the Brin-Thompson groups $nV$, among many others. We offer a unified construction of geometric models for $Γ_{S}$ and a general framework for studying the finiteness properties of these groups.
