Embedding universality for II1 factors with property (T)

We prove that every separable tracial von Neumann algebra embeds into a II1 factor with property (T) which can be taken to have trivial outer automorphism and fundamental groups. also establish an analogous result for the extension over non-atomic probability space of countable p.m.p. equivalence relation. In addition, we obtain two new results concerning structure infinitely generic factors. These are obtained by using class wreath-like product groups introduced recently in [8].