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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2304.07656 |
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| _version_ | 1866929625651740672 |
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| author | Arzhantseva, Goulnara Paunescu, Liviu |
| author_facet | Arzhantseva, Goulnara Paunescu, Liviu |
| contents | An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We extend such a characterisation to constraint stability. We give sufficient conditions for a group to be constraint stable. As an application, we obtain many new examples of groups stable in permutations, in particular, among free amalgamated products over a finite group. This is the first general result (besides trivial case of free products) which gives a wealth of non-amenable groups stable in permutations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2304_07656 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constraint stability in permutations and action traces Arzhantseva, Goulnara Paunescu, Liviu Group Theory Functional Analysis Operator Algebras 20Fxx, 20F05, 20F69, 20B30, 22F10 An action trace is a function naturally associated to a probability measure preserving action of a group on a standard probability space. For countable amenable groups, we characterise stability in permutations using action traces. We extend such a characterisation to constraint stability. We give sufficient conditions for a group to be constraint stable. As an application, we obtain many new examples of groups stable in permutations, in particular, among free amalgamated products over a finite group. This is the first general result (besides trivial case of free products) which gives a wealth of non-amenable groups stable in permutations. |
| title | Constraint stability in permutations and action traces |
| topic | Group Theory Functional Analysis Operator Algebras 20Fxx, 20F05, 20F69, 20B30, 22F10 |
| url | https://arxiv.org/abs/2304.07656 |