JournalsggdVol. 4, No. 2pp. 377–405

On a series of finite automata defining free transformation groups

  • Mariya Vorobets

    Texas A&M University, College Station, USA
  • Yaroslav Vorobets

    Texas A&M University, College Station, USA
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Abstract

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. 377–405

DOI 10.4171/GGD/87