On a series of finite automata defining free transformation groups

Details On a series of finite automata defining free transformation groups On a series of finite automata defining free transformation groups

2006-04-14

arxiv.org/abs/math/0604328v1

Mathematics

Group Theory

36 pages, 8 figures

Scientific paper

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.

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