连通三态可逆Mealy自动机不能生成无限Burnside群
A connected 3-state reversible Mealy automaton cannot generate an infinite Burnside group
摘要：
自动机群类是无限伯恩赛德群最简单例子的丰富来源。然而，有一些自动机类不包含这样的例子。例如，所有文献中的无限Burnside自动机群都是由不可逆Mealy自动机生成的，最近证明了2-状态可逆-可逆Mealy自动机不能生成无限Burnside群。在这里，我们将这一结果连接3状态可逆可逆Mealy自动机，使用新的原始技术。这些结果为构造这类无限群中的无限阶元提供了第一个统一的方法。
英文摘要：
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples. For instance, all infinite Burnside automaton groups in the literature are generated by non reversible Mealy automata and it was recently shown that 2-state invertible-reversible Mealy automata cannot generate infinite Burnside groups. Here we extend this result to connected 3-state invertible-reversible Mealy automata, using new original techniques. The results provide the first uniform method to construct elements of infinite order in each infinite group in this class.
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。
