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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.

##### MSC:
 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
##### Software:
FR; AutomGrp; GAP
Full Text:
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