Testability in group theory
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866910520498454528 |
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| author | Becker, Oren Lubotzky, Alexander Mosheiff, Jonathan |
| author_facet | Becker, Oren Lubotzky, Alexander Mosheiff, Jonathan |
| contents | This paper is a journal counterpart to our FOCS 2021 paper, in which we initiate the study of property testing problems concerning a finite system of relations $E$ between permutations, generalizing the study of stability in permutations. To every such system $E$, a group $Γ=Γ_E$ is associated and the testability of $E$ depends only on $Γ$ (just like in Galois theory, where the solvability of a polynomial is determined by the solvability of the associated group). This leads to the notion of testable groups, and, more generally, Benjamini-Schramm rigid groups. The paper presents an ensemble of tools to check if a given group $Γ$ is testable/BS-rigid or not. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2204_04539 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Testability in group theory Becker, Oren Lubotzky, Alexander Mosheiff, Jonathan Group Theory Data Structures and Algorithms Combinatorics This paper is a journal counterpart to our FOCS 2021 paper, in which we initiate the study of property testing problems concerning a finite system of relations $E$ between permutations, generalizing the study of stability in permutations. To every such system $E$, a group $Γ=Γ_E$ is associated and the testability of $E$ depends only on $Γ$ (just like in Galois theory, where the solvability of a polynomial is determined by the solvability of the associated group). This leads to the notion of testable groups, and, more generally, Benjamini-Schramm rigid groups. The paper presents an ensemble of tools to check if a given group $Γ$ is testable/BS-rigid or not. |
| title | Testability in group theory |
| topic | Group Theory Data Structures and Algorithms Combinatorics |
| url | https://arxiv.org/abs/2204.04539 |