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For each group $G$ having an infinite normal subgroup with the relativeproperty (T) (for instance $G = H \times K$ where $H$ is infinite with property(T) and $K$ is arbitrary), and any countable abelian group $\Lambda$ weconstruct free ergodic measure preserving actions $\sigma_\Lambda$ of $G$ onthe probability space such that the 1'st cohomology group of $\sigma_\Lambda$,$H^1(\sigma_\Lambda)$, is equal to Char$(G) \times \Lambda$. We deduce that $G$has uncountably many non stably orbit equivalent actions. We also calculate1-cohomology groups and show existence of ``many'' non stably orbit equivalentactions for free products of groups as above.

SOME COMPUTATIONS OF 1-COHOMOLOGY GROUPS AND CONSTRUCTION OF NON-ORBIT-EQUIVALENT ACTIONS