论文标题
本地置换稳定性
Local permutation stability
论文作者
论文摘要
我们引入了有限生成的组的“局部稳定性”的概念。如果一组在我们的意义上是Sofic且本地稳定的，则它也可以局部嵌入到有限的组中（LEF）。我们的概念比Glebsky-Rivera和Arzhantseva-Paunescu引入的“置换稳定性”弱，这使人们可以升级Soficities至残留的有限性。我们证明，就不变的随机亚组（IRS）而言，可延迟的群体是局部置换稳定的必要条件，这是受贝克尔，卢博兹基和汤姆引起的类似置换稳定性的启发。我们应用我们的标准证明，使用Zheng对这些组的IRS进行分类，局部最小的子迁移的拓扑完整群体的衍生子组在本地稳定。最后的结果提供了当地稳定但不稳定的连续群体。
We introduce a notion of "local stability in permutations" for finitely generated groups. If a group is sofic and locally stable in our sense, then it is also locally embeddable into finite groups (LEF). Our notion is weaker than the "permutation stability" introduced by Glebsky-Rivera and Arzhantseva-Paunescu, which allows one to upgrade soficity to residual finiteness. We prove a necessary and sufficient condition for an amenable group to be locally permutation stable, in terms of invariant random subgroups (IRSs), inspired by a similar criterion for permutation stability due to Becker, Lubotzky and Thom. We apply our criterion to prove that derived subgroups of topological full groups of Cantor minimal subshifts are locally stable, using Zheng's classification of IRSs for these groups. This last result provides continuum-many groups which are locally stable, but not stable.
