有限型移位上的周期点与群的可公度不变量
Periodic Points on Shifts of Finite Type and Commensurability Invariants of Groups
摘要：
我们探讨了子群和可以定义在群上的有限型（SFT）的可能移位之间的关系。特别是，我们研究了两个群不变量，弱周期性和强周期性，通过符号动力学定义的组。我们表明，这些属性是不变量的可扩展性。因此，许多已知的关于定义在群上的SFT中的周期点的结果实际上是关于整个可并行性类的结果。此外，我们表明，不强周期性（也称为弱非周期性）的性质是保留下的扩展与生成的内核。最后，我们提出的问题，这些不变量的关系，准等距和增长的几何概念。
英文摘要：
We explore the relationship between subgroups and the possible shifts of finite type (SFTs) that can be defined on the group. In particular, we investigate two group invariants, weak periodicity and strong periodicity, defined via symbolic dynamics on the group. We show that these properties are invariants of commensurability. Thus, many known results about periodic points in SFTs defined over groups are actually results about entire commensurability classes. Additionally, we show that the property of being not strongly periodic (also called weakly aperiodic) is preserved under extensions with finitely generated kernels. We conclude by raising questions and conjectures about the relationship of these invariants to the geometric notions of quasi-isometry and growth.
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