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 |
| _version_ | 1817994331062009856 |
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| author | Tom Meyerovitch |
| author_facet | Tom Meyerovitch |
| author_sort | Tom Meyerovitch |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-14T01:50:37Z |
| format | Article |
| id | doaj.art-4153287e879c403ea6d173b34423490e |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-04-14T01:50:37Z |
| publishDate | 2016-07-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-4153287e879c403ea6d173b34423490e2022-12-22T02:19:21ZengMDPI AGEntropy1099-43002016-07-0118726310.3390/e18070263e18070263Positive Sofic Entropy Implies Finite StabilizerTom Meyerovitch0Department of Mathematics, Ben-Gurion University of the Negev, Be’er Sheva 8410501, IsraelWe 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.http://www.mdpi.com/1099-4300/18/7/263sofic entropystabilizersinvariant random subgroups |
| spellingShingle | Tom Meyerovitch Positive Sofic Entropy Implies Finite Stabilizer Entropy sofic entropy stabilizers invariant random subgroups |
| title | Positive Sofic Entropy Implies Finite Stabilizer |
| title_full | Positive Sofic Entropy Implies Finite Stabilizer |
| title_fullStr | Positive Sofic Entropy Implies Finite Stabilizer |
| title_full_unstemmed | Positive Sofic Entropy Implies Finite Stabilizer |
| title_short | Positive Sofic Entropy Implies Finite Stabilizer |
| title_sort | positive sofic entropy implies finite stabilizer |
| topic | sofic entropy stabilizers invariant random subgroups |
| url | http://www.mdpi.com/1099-4300/18/7/263 |
| work_keys_str_mv | AT tommeyerovitch positivesoficentropyimpliesfinitestabilizer |