Abstract
We prove that every linear-activity automaton group is amenable. The proof is based on showing that a random walk on a specially constructed degree 1 automaton group-the mother group-has asymptotic entropy 0. Our result answers an open question by Nekrashevych in the Kourovka notebook, and gives a partial answer to a question of Sidki.
| Original language | English |
|---|---|
| Pages (from-to) | 705-730 |
| Number of pages | 26 |
| Journal | Journal of the European Mathematical Society |
| Volume | 15 |
| Issue number | 3 |
| DOIs | |
| State | Published - 2013 |
Funding
| Funders | Funder number |
|---|---|
| National Science Foundation | 0206781 |
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