论文标题
图自动机组
Graph automaton groups
论文作者
论文摘要
在本文中，我们定义了从有限图开始获得有限的可逆自动机的方法。事实证明，相应的自动机组是其换向器子组的常规弱分支，在两个元素上包含一个自由的半群，并且可以接受指数增长。我们还强调了我们的构建与右角Artin团体之间的联系。然后，我们研究与这些自动机组在常规生根树上的自相似作用相关的Schreier图。在初始图是一条路径的情况下，我们明确确定其直径及其自动形态组。此外，我们表明，循环的情况产生了Schreier图，其自动形态群对二面体是同构的。值得注意的是，我们的构造恢复了一些自动机组的经典示例，例如添加机和纠结的里程表。
In this paper we define a way to get a bounded invertible automaton starting from a finite graph. It turns out that the corresponding automaton group is regular weakly branch over its commutator subgroup, contains a free semigroup on two elements and is amenable of exponential growth. We also highlight a connection between our construction and the right-angled Artin groups. We then study the Schreier graphs associated with the self-similar action of these automaton groups on the regular rooted tree. We explicitly determine their diameter and their automorphism group in the case where the initial graph is a path. Moreover, we show that the case of cycles gives rise to Schreier graphs whose automorphism group is isomorphic to the dihedral group. It is remarkable that our construction recovers some classical examples of automaton groups like the Adding machine and the Tangled odometer.
