Positive sofic entropy implies finite stabilizer
Dynamical Systems
2016-08-24 v3 Group Theory
Abstract
We prove that for a measure preserving action of a sofic group with positive sofic entropy, the set of points with finite stabilizer have positive measure. This extends results of Weiss and Seward for amenable groups and free groups, respectively. It follows that the action of a sofic group on its subgroups by inner automorphisms has zero topological sofic entropy, and a faithful action with completely positive sofic entropy must be free.
Cite
@article{arxiv.1504.08137,
title = {Positive sofic entropy implies finite stabilizer},
author = {Tom Meyerovitch},
journal= {arXiv preprint arXiv:1504.08137},
year = {2016}
}
Comments
14 Pages. Some typo corrections