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Orbit automata as a new tool to attack the order problem in automaton groups. (English) Zbl 1383.20018
Summary: 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.

20F10 Word problems, other decision problems, connections with logic and automata (group-theoretic aspects)
20M35 Semigroups in automata theory, linguistics, etc.
20E08 Groups acting on trees
68Q70 Algebraic theory of languages and automata
68Q45 Formal languages and automata
FR; AutomGrp; GAP
Full Text: DOI arXiv
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