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We introduce a new tool, called the orbit automaton, that describes theaction 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 generatedby the orbit automata is used to find elements of infinite order in certainautomaton groups for which other methods failed to work.

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