Similarity degree of type II${}_1$ von Neumann algebras with Property $\mathrm{\Gamma }$

In this paper, we discuss some equivalent definitions of Property $\mathrm{\Gamma }$ for a type II${}_1$ von Neumann algebra. Using these equivalent definitions, we prove that the Pisier’s similarity degree of a type II${}_1$ von Neumann algebra with Property $\mathrm{\Gamma }$ is equal to $3$.