Journal of Fractal Geometry

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Volume 4, Issue 4, 2017, pp. 425–458
DOI: 10.4171/JFG/56

Published online: 2017-12-05

Full groups of bounded automaton groups

Nicolás Matte Bon[1]

(1) ETH Zürich, Switzerland

We show that every bounded automaton group can be embedded in a finitely generated, simple amenable group. The proof is based on the study of the topological full groups associated to the Schreier dynamical system of the mother groups. We also show that if $\mathcal{G}$ is a minimal étale groupoid with unit space the Cantor set, the group $[[\mathcal{G}]]_t$ generated by all torsion elements in the topological full group has simple commutator subgroup.

Keywords: Self-similar groups, amenability, simple group, Schreier graph, étale groupoid, Bratteli diagram

Matte Bon Nicolás: Full groups of bounded automaton groups. J. Fractal Geom. 4 (2017), 425-458. doi: 10.4171/JFG/56