Let $G,H$ be two countable amenable groups. We introduce the notion of group charts, which gives us a tool to embed an arbitrary $H$-subshift into a $G$-subshift. Using an entropy addition formula derived from this formalism we prove that whenever $H$ is finitely presented and admits a subshift of finite type (SFT) on which $H$ acts freely, then the set of real numbers attained as topological entropies of $H$-SFTs is contained in the set of topological entropies of $G$-SFTs modulo an arbitrarily small additive constant for any finitely generated group $G$ which admits a translation-like action of $H$. In particular, we show that the set of topological entropies of $G$-SFTs on any such group which has decidable word problem and admits a translation-like action of $\mathbb{Z}^2$ coincides with the set of non-negative upper semi-computable real numbers. We use this result to give a complete characterization of the entropies of SFTs in several classes of groups.

中文翻译：

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关于可数服从群上有限类型子移的熵

令 $G,H$ 是两个可数的服从组。我们引入了组图的概念，它为我们提供了一种将任意 $H$-subshift 嵌入到 $G$-subshift 中的工具。使用从这种形式主义导出的熵加法公式，我们证明只要 $H$ 被有限地呈现并允许 $H$ 自由作用于其上的有限类型 (SFT) 的子移，那么作为 $H$ 的拓扑熵获得的实数集$-SFTs 包含在 $G$-SFTs 的拓扑熵集合中，对任何有限生成的群 $G$ 取模一个任意小的加性常数，它允许 $H$ 的平移动作。特别是，我们证明 $G$-SFTs 在任何具有可判定词问题并承认 $\mathbb{Z}^2$ 的类翻译动作的组上的拓扑熵集与非负上半数集一致- 可计算的实数。我们使用这个结果给出了几类群中 SFT 熵的完整表征。