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Entropy 2016, 18(7), 263; doi:10.3390/e18070263

Positive Sofic Entropy Implies Finite Stabilizer

Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva 8410501, Israel
Academic Editor: Tomasz Downarowicz
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)
View Full-Text   |   Download PDF [282 KB, uploaded 18 July 2016]

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. View Full-Text
Keywords: sofic entropy; stabilizers; invariant random subgroups sofic entropy; stabilizers; invariant random subgroups
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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

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