Testability in group theory

04/09/2022

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by   Oren Becker, et al.

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Hebrew University of Jerusalem

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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.