Positive Sofic Entropy Implies Finite Stabilizer
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 subg...
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| Format: | Article |
| Language: | English |
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MDPI AG
2016-07-01
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| Series: | Entropy |
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| Online Access: | http://www.mdpi.com/1099-4300/18/7/263 |
| Summary: | 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. |
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| ISSN: | 1099-4300 |