Some non-contracting automata groups

2013/11/14 by Nick Davis, Davis, Nick, Murray Elder +3
Biochemistry, Genetics and Molecular Biology · Computer Science · Mathematics · #20F65 #Chemical Synthesis and Analysis #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1311.3362

openalex publication_date 2013/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 implies that the associated self-similarity graph introduced by Nekrashevych is non-hyperbolic.

Related

• Classification of groups generated by 3-state automata over a 2-letter alphabet
• Groups generated by 3-state automata over a 2-letter alphabet, II
• Groups generated by 3-state automata over a 2-letter alphabet, I
• Self-similar groups acting essentially freely on the boundary of the binary rooted tree
• The word and order problems for self-similar and automata groups