Geodesic
Non-contracting groups generated by (3,2)-automata
Algebra and discrete mathematics, Tome 17 (2014) no. 1, pp. 20-32.

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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: self-similar group, contracting action, self-similarity graph.
Mots-clés : automaton group 
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Nick Davis; Murray Elder; Lawrence Reeves. Non-contracting  groups generated by (3,2)-automata. Algebra and discrete mathematics, Tome 17 (2014) no. 1, pp. 20-32. http://geodesic.mathdoc.fr/item/ADM_2014_17_1_a2/

[1] Ievgen Bondarenko, Rostislav Grigorchuk, Rostyslav Kravchenko, Yevgen Muntyan, Volodymyr Nekrashevych, Dmytro Savchuk, and Zoran Šunić, “On classification of groups generated by 3-state automata over a 2-letter alphabet”, Algebra Discrete Math., 2008, no. 1, 1–163 | MR | Zbl

[2] Martin R. Bridson and André Haefliger, Metric spaces of non-positive curvature, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], 319, Springer-Verlag, Berlin, 1999 | MR | Zbl

[3] Yevgen Muntyan, Automata Groups, PhD thesis, Texas A University, 2009 | MR

[4] Volodymyr Nekrashevych, “Self-similar groups”, Mathematical Surveys and Monographs, 117, American Mathematical Society, Providence, RI, 2005 | MR