Abstract
We prove that, for a measure preserving action of a sofic group with positive sofic entropy, the stabilizer is finite on a set of positive measures. This extends the 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 that a faithful action that has completely positive sofic entropy must be free.
Original language | American English |
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Article number | 263 |
Journal | Entropy |
Volume | 18 |
Issue number | 7 |
DOIs | |
State | Published - 18 Jul 2016 |
Keywords
- Invariant random subgroups
- Sofic entropy
- Stabilizers
All Science Journal Classification (ASJC) codes
- General Physics and Astronomy