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We prove that every separable tracial von Neumann algebra embeds into aII$_1$ factor with property (T) which can be taken to have trivial outerautomorphism and fundamental groups. We also establish an analogous result forthe trivial extension over a non-atomic probability space of every countablep.m.p. equivalence relation. These results are obtained by using the class ofwreath-like product groups introduced recently in \cite{CIOS21}.

Embedding universality for II$_1$ factors with property (T)