Kazhdan群的软逼近的中心化子
Centralizers of sofic approximations of Kazhdan groups
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中文总结 AI 辅助
该研究证明了满足特定软嵌入条件的Kazhdan群局部可嵌入有限群，有限呈现的此类群为剩余有限，并得出其软嵌入的中心化子是置换群度量超积的结论。
中文摘要 AI 辅助
我们证明，若一个Kazhdan群允许在对称群的度量超积中进行软嵌入，且该嵌入的中心化子在相关Loeb概率空间上遍历作用，则该群局部可嵌入有限群（LEF）。特别地，每个允许此类嵌入的有限呈现Kazhdan群都是剩余有限的。主要技术定理指出，Kazhdan群的软嵌入的中心化子本身就是置换群的度量超积。
英文摘要
We prove that a Kazhdan group admitting a sofic embedding into a metric ultraproduct of symmetric groups with a centralizer that acts ergodically on the associated Loeb probability space is locally embeddable in finite groups (LEF). In particular, every finitely presented Kazhdan group admitting such an embedding is residually finite. The main technical theorem says that the centralizer of a sofic embedding of a Kazhdan group is itself a metric ultraproduct of permutation groups.
