On a series of finite automata defining free transformation groups
Mariya Vorobets, Yaroslav Bogdanovich Vorobets · Groups Geometry and Dynamics · 2010
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.