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.
Cite this article
Mariya Vorobets, Yaroslav Vorobets, On a series of finite automata defining free transformation groups. Groups Geom. Dyn. 4 (2010), no. 2, pp. 377–405DOI 10.4171/GGD/87