On a series of finite automata defining free transformation groups
Group Theory
2007-05-23 v1
Abstract
We introduce two series of finite automata starting from the so-called Aleshin and Bellaterra automata. We prove that each automaton in the first series defines a free non-Abelian group while each automaton in the second series defines the free product of groups of order 2. Furthermore, these properties are shared by disjoint unions of any number of distinct automata from either series.
Keywords
Cite
@article{arxiv.math/0604328,
title = {On a series of finite automata defining free transformation groups},
author = {Mariya Vorobets and Yaroslav Vorobets},
journal= {arXiv preprint arXiv:math/0604328},
year = {2007}
}
Comments
36 pages, 8 figures