On classification of groups generated by \(3\)-state automata over a \(2\)-letter alphabet

• Date: 2018
• Main Authors: Bondarenko, Ievgen, Grigorchuk, Rostislav, Kravchenko, Rostyslav, Muntyan, Yevgen, Nekrashevych, Volodymyr, Savchuk, Dmytro, Sunic, Zoran
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: automata groups; self-similar groups; branch groups; 20E08
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/805
• Journal Title: Algebra and Discrete Mathematics

We show that the class of groups generated by 3-state automata over a 2-letter alphabet has no more than 122 members. For each group in the class we provide some basic information, such as short relators, a few initial values of the growth function, a few initial values of the sizes of the quotients...