On amenability of automata groups

Details On amenability of automata groups On amenability of automata groups

2008-02-20

arxiv.org/abs/0802.2837v1

Duke Math. J. Volume 154, Number 3 (2010), 575-598

Mathematics

Group Theory

Scientific paper

10.1215/00127094-2010-046

We show that the group of bounded automatic automorphisms of a rooted tree is
amenable, which implies amenability of numerous classes of groups generated by
finite automata. The proof is based on reducing the problem to showing
amenability just of a certain explicit family of groups ("Mother groups") which
is done by analyzing the asymptotic properties of random walks on these groups.

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