Some non-contracting automata groups
Group Theory
2013-11-15 v1
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.
Cite
@article{arxiv.1311.3362,
title = {Some non-contracting automata groups},
author = {Nick Davis and Murray Elder and Lawrence Reeves},
journal= {arXiv preprint arXiv:1311.3362},
year = {2013}
}
Comments
9 pages