  We provide a unified and self-contained treatment of several of the recent
uniqueness theorems for the group measure space decomposition of a II_1 factor.
We single out a large class of groups \Gamma, characterized by a one-cohomology
property, and prove that for every free ergodic probability measure preserving
action of \Gamma the associated II_1 factor has a unique group measure space
Cartan subalgebra up to unitary conjugacy. Our methods follow closely a recent
article of Chifan-Peterson, but we replace the usage of Peterson's unbounded
derivations by Thomas Sinclair's dilation into a one-parameter group of
automorphisms.
