Amenability of groups is characterized by Myhill's Theorem
Amenability of groups is characterized by Myhill's Theorem
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DOI：
10.4171/jems/900
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发表时间：
2016-05
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影响因子：
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通讯作者：
L. Bartholdi
中科院分区：
文献类型：
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作者：
L. Bartholdi
我们证明了一个匡威Myhill的“伊甸园”定理，并以这种方式获得一个表征的顺从性方面的细胞自动机：“一组$G$是顺从的，当且仅当每一个细胞自动机与承运人$G$有伊甸园也有相互可擦除的模式。这回答了Schupp的一个问题，解决了Ceccherini-Silberstein，Mach和Scarabotti的一个猜想。一个附录由达维德Kielak证明，群环没有零因子是Ore域正是当组是顺从的，回答了一个猜想归因于古巴。
We prove a converse to Myhill's "Garden-of-Eden" theorem and obtain in this manner a characterization of amenability in terms of cellular automata: "A group $G$ is amenable if and only if every cellular automaton with carrier $G$ that has gardens of Eden also has mutually erasable patterns." This answers a question by Schupp, and solves a conjecture by Ceccherini-Silberstein, Mach\`i and Scarabotti. An appendix by Dawid Kielak proves that group rings without zero divisors are Ore domains precisely when the group is amenable, answering a conjecture attributed to Guba.