On a series of finite automata defining free transformation groups

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We introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata. We prove that each automaton in the first series defines a free non-Abelian group while each automaton in the second series defines the free product of groups of order 2. Furthermore, these properties are shared by disjoint unions of any number of distinct automata from either series.
36 pages, 8 figures

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Group Theory, 20E05; 20E08

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http://salesiana.dossiersoluciones.com/handle/123456789/111572

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0604328
 http://arxiv.org/abs/math/0604328

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arXiv