论文标题
群体理论可检验性
Testability in group theory
论文作者
论文摘要
本文是与我们的2021纸相对的杂志，在该论文中，我们启动了有关在排列之间涉及有限关系系统$ e $的财产测试问题的研究，从而推广了排列中稳定性的研究。对于每个这样的系统$ e $，$γ=γ_e$都关联，并且$ e $的可检验性仅取决于$γ$（就像在Galois理论中一样，多项式的可溶性由相关组的溶解度确定）。这导致了可测试组的概念，更普遍地是本杰米尼 - 施拉姆刚性组的概念。该论文提供了一组工具，以检查给定的$γ$是否可以测试/bs-rigid。
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.
