Abstract
We prove that the boundary dynamics of the (semi)group generated by the enriched dual transducer characterizes the algebraic property of being free for an automaton group. We specialize this result to the class of bireversible transducers and we show that the property of being not free is equivalent to the existence of a finite Schreier graph in the boundary of the enriched dual pointed at some essentially non-trivial point. From these results we derive some consequences from the algebraic, algorithmic and dynamical points of view.
Original language | English |
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Pages (from-to) | 115-136 |
Number of pages | 22 |
Journal | Journal of Algebra |
Volume | 462 |
DOIs | |
Publication status | Published - 15 Sept 2016 |
Keywords
- Automaton groups
- Boundary actions
- Essentially free actions
- Schreier graphs
ASJC Scopus subject areas
- Algebra and Number Theory