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arXiv · 1311.3362

Some non-contracting automata groups

Nick Davis·Murray Elder·Lawrence Reeves
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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.

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Nick Davis, Murray Elder, Lawrence Reeves. 2013-11-14. Some non-contracting automata groups. https://arxiv.org/abs/1311.3362

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