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Algebra and Discrete Mathematics, 2014, Volume 17, Issue 1, Pages 20–32
(Mi adm457)
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RESEARCH ARTICLE
Non-contracting groups generated by (3,2)-automata
Nick Davisa, Murray Elderb, Lawrence Reevesa a 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.
Received: 29.11.2013 Revised: 29.11.2013
Citation:
Nick Davis, Murray Elder, Lawrence Reeves, “Non-contracting groups generated by (3,2)-automata”, Algebra Discrete Math., 17:1 (2014), 20–32
Linking options:
https://www.mathnet.ru/eng/adm457 https://www.mathnet.ru/eng/adm/v17/i1/p20
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Statistics & downloads: |
Abstract page: | 290 | Full-text PDF : | 114 | References: | 38 |
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