Groups, Geometry, and Dynamics


Full-Text PDF (318 KB) | Metadata | Table of Contents | GGD summary
Volume 4, Issue 2, 2010, pp. 377–405
DOI: 10.4171/GGD/87

Published online: 2010-02-21

On a series of finite automata defining free transformation groups

Mariya Vorobets[1] and Yaroslav Vorobets[2]

(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