Positive sofic entropy implies finite stabilizer

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


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
Issue number7
StatePublished - 18 Jul 2016


  • Invariant random subgroups
  • Sofic entropy
  • Stabilizers

ASJC Scopus subject areas

  • Physics and Astronomy (all)


Dive into the research topics of 'Positive sofic entropy implies finite stabilizer'. Together they form a unique fingerprint.

Cite this