Orbit automata as a new tool to attack the order problem in automaton groups
Group Theory
2014-12-04 v2 Formal Languages and Automata Theory
Abstract
We introduce a new tool, called the orbit automaton, that describes the action of an automaton group on the subtrees corresponding to the orbits of on levels of the tree. The connection between and the groups generated by the orbit automata is used to find elements of infinite order in certain automaton groups for which other methods failed to work.
Keywords
Cite
@article{arxiv.1411.0158,
title = {Orbit automata as a new tool to attack the order problem in automaton groups},
author = {Ines Klimann and Matthieu Picantin and Dmytro Savchuk},
journal= {arXiv preprint arXiv:1411.0158},
year = {2014}
}
Comments
19 pages, 9 figures; example with Bellaterra group added; references updated