Centralizers of sofic approximations of Kazhdan groups

2026/08/05 by Vadim Alekseev, Andreas Thom · 1 citation
Mathematics · #math.GR #msc:20F65 #msc:20F69 #msc:20F05 #msc:37A15 #msc:46L10

paper · pdf

19 pages, no figures

arxiv created 2026/08/05 · arxiv updated 2026/08/07

Abstract

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.

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