Positive sofic entropy implies finite stabilizer

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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 languageEnglish
Article number263
JournalEntropy
Volume18
Issue number7
DOIs
StatePublished - 1 Jul 2016

Keywords

  • Invariant random subgroups
  • Sofic entropy
  • Stabilizers

ASJC Scopus subject areas

  • Physics and Astronomy (all)

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