Finite von Neumann Algebra Factors with Property Γ

Techniques introduced by G. Pisier in his proof that finite von Neumann factors with property Γ have length at most 5 are modified to prove that the length is 3. It is proved that if such a factor is a complemented subspace of a larger C*-algebra then there exists a projection of norm one from the larger algebra onto the smaller and a new proof of the fact that the continuous Hochschild cohomology group H2c(M, M) vanishes is also included.