元胞自动机的图积与圈积
Graph and wreath products of cellular automata
AI总结：
本文证明了双侧全移位自同构群的子群在可数图积下封闭，引入无 $A$-消除的群作用概念，并证明有限阿贝尔群与元胞自动机群的圈积可嵌入全移位自同构群，同时将结论推广至单侧情形。
摘要：
我们证明双侧全移位自同构群的子群集合在可数图积下是封闭的。我们引入无 $A$-消除（对于阿贝尔群 $A$）的群作用概念，并证明当 $A$ 为有限阿贝尔群且 $G$ 为作用无 $A$-消除的元胞自动机群时，圈积 $A \wr G$ 可嵌入全移位的自同构群中。我们证明所有自由阿贝尔群和自由群均存在此类元胞自动机作用。对于单侧情形，我们在合理的字母表扩展下证明了这些结果的变体。
英文摘要：
We prove that the set of subgroups of the automorphism group of a two-sided full shift is closed under countable graph products. We introduce the notion of a group action without $A$-cancellation (for an abelian group $A$), and show that when $A$ is a finite abelian group and $G$ is a group of cellular automata whose action does not have $A$-cancellation, the wreath product $A \wr G$ embeds in the automorphism group of a full shift. We show that all free abelian groups and free groups admit such cellular automata actions. In the one-sided case, we prove variants of these results with reasonable alphabet blow-ups.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
