群论中的可测试性
Testability in group theory
AI总结：
该研究将置换稳定性研究推广到置换间有限关系系统的属性测试，发现其可测试性由对应群决定，提出可测试群与Benjamini-Schramm刚性群概念，并给出检验群是否具备该性质的工具集。
摘要：
本文是我们发表于FOCS 2021的论文的期刊版，在那篇论文中，我们首次研究了与置换间有限关系系统$E$相关的属性测试问题，推广了置换稳定性的研究。每个此类系统$E$都对应一个群$Γ=Γ_E$，且$E$的可测试性仅由$Γ$决定（就像伽罗瓦理论中，多项式的可解性由对应群的可解性决定一样）。这引出了可测试群的概念，以及更广义的Benjamini-Schramm刚性群。本文提出了一套工具，用于检验给定群$Γ$是否具有可测试性/BS刚性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
