Non-contracting groups generated by (3,2)-automata

• Date: 2018
• Main Authors: Davis, Nick, Elder, Murray, Reeves, Lawrence
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: automaton group; self-similar group; contracting action; self-similarity graph; 20E08; 20F65; 68Q45
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/1022
• Journal Title: Algebra and Discrete Mathematics

We add to the classification of groups generated by 3-state automata over a 2-letter alphabet given by Bondarenko \( et \ al.\), by showing that a number of the groups in the classification are non-contracting. We show that the criterion we use to prove a self-similar action is non-contracting also...