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arXiv · 1411.0158

Orbit automata as a new tool to attack the order problem in automaton groups

Ines Klimann·Matthieu Picantin·Dmytro Savchuk
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Abstract

We introduce a new tool, called the orbit automaton, that describes the action of an automaton group $G$ on the subtrees corresponding to the orbits of $G$ on levels of the tree. The connection between $G$ 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.

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Ines Klimann, Matthieu Picantin, Dmytro Savchuk. 2014-12-03. Orbit automata as a new tool to attack the order problem in automaton groups. https://arxiv.org/abs/1411.0158

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