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arXiv · 2204.04539

Testability in group theory

Oren Becker·Alexander Lubotzky·Jonathan Mosheiff
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Abstract

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 $\Gamma=\Gamma_E$ is associated and the testability of $E$ depends only on $\Gamma$ (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 $\Gamma$ is testable/BS-rigid or not.

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BibTeXRIS

Oren Becker, Alexander Lubotzky, Jonathan Mosheiff. 2022-04-09. Testability in group theory. https://doi.org/10.1007/s11856-023-2503-y

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