We obtain the following embedding theorem for symbolic dynamical systems. Let G be a countable amenable group with the comparison property. Let X be a strongly aperiodic subshift over G. Let Y be a strongly irreducible shift of finite type over G that has no global period, meaning that the shift action is faithful on Y. If the topological entropy of X is strictly less than that of Y and Y contains at least one factor of X, then X embeds into Y. This result partially extends the classical result of Krieger when $G = \mathbb {Z}$ and the results of Lightwood when $G = \mathbb {Z}^d$ for $d \geq 2$ . The proof relies on recent developments in the theory of tilings and quasi-tilings of amenable groups.

中文翻译：

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具有比较性质的服从群上的子平移嵌入定理

我们得到以下符号动力系统的嵌入定理。让G是具有比较性质的可数服从群。让X是一个强非周期性子移G。让是是有限类型的强不可约移位G没有全局周期，这意味着换档动作忠实于是。如果拓扑熵为X严格小于是和是至少包含一个因素X， 然后X嵌入到是。该结果部分扩展了 Krieger 的经典结果，当 $G = \mathbb {Z}$ 以及 Lightwood 时的结果 $G = \mathbb {Z}^d$ 为了 $d \geq 2$ 。该证明依赖于顺应群的平铺和准平铺理论的最新发展。