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Open AccessArticle

Positive Sofic Entropy Implies Finite Stabilizer

Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva 8410501, Israel
Academic Editor: Tomasz Downarowicz
Entropy 2016, 18(7), 263; https://doi.org/10.3390/e18070263
Received: 1 May 2016 / Revised: 11 July 2016 / Accepted: 14 July 2016 / Published: 18 July 2016
(This article belongs to the Special Issue Entropic Properties of Dynamical Systems)
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. View Full-Text
Keywords: sofic entropy; stabilizers; invariant random subgroups sofic entropy; stabilizers; invariant random subgroups
MDPI and ACS Style

Meyerovitch, T. Positive Sofic Entropy Implies Finite Stabilizer. Entropy 2016, 18, 263.

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