RESEARCH ARTICLE

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

Nick Davis^a, Murray Elder^b, Lawrence Reeves<sup>a

a</sup> Department of Mathematics and Statistics, University of Melbourne, Parkville VIC 3010, Australia
^b School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan NSW 2308, Australia

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.

Keywords: automaton group, self-similar group, contracting action, self-similarity graph.

MSC: 20E08, 20F65, 68Q45

Received: 29.11.2013
Revised: 29.11.2013

Language: English

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