A Kazhdan group with a sofic embedding having an ergodic centralizer is LEF; finitely presented examples are residually finite.
de Cornulier,Finitely presentable, non-Hopfian groups with Kazhdan’s property (T) and infinite outer automorphism group, Proc
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Centralizers of sofic approximations of Kazhdan groups
A Kazhdan group with a sofic embedding having an ergodic centralizer is LEF; finitely presented examples are residually finite.