Amenability of linear-activity automaton groups
Group Theory
2013-07-24 v2 Probability
Abstract
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a sufficiently symmetric random walk on a specially constructed degree 1 automaton group -- the mother group -- has asymptotic entropy 0. Our result answers an open question by Nekrashevich in the Kourovka notebook, and gives a partial answer to a question of Sidki.
Keywords
Cite
@article{arxiv.0905.2007,
title = {Amenability of linear-activity automaton groups},
author = {Gideon Amir and Omer Angel and Balint Virag},
journal= {arXiv preprint arXiv:0905.2007},
year = {2013}
}
Comments
29 pages, 1 figure. Revised version after referee report. To appear in the Journal of the European Mathematical Society