Groups, Geometry, and Dynamics
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Published online: 2010-02-21
On a series of finite automata defining free transformation groupsMariya Vorobets and Yaroslav Vorobets (1) Texas A&M University, College Station, USA
(2) Texas A&M University, College Station, USA
We introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata. We prove that transformations defined by automata from the first series generate a free non-Abelian group of infinite rank, while automata from the second series give rise to the free product of infinitely many groups of order 2.
Keywords: Automaton group, free non-Abelian group, finite automaton
Vorobets Mariya, Vorobets Yaroslav: On a series of finite automata defining free transformation groups. Groups Geom. Dyn. 4 (2010), 377-405. doi: 10.4171/GGD/87