2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/144783We prove that if a countable group $Γ$ contains infinite commuting subgroups $H, H'\subset Γ$ with $H$ non-amenable and $H'$ ``weakly normal'' in $Γ$, then any measure preserving $Γ$-action on a probability space which satisfies certain malleability, spectral gap and weak mixing conditions (e.g. a Bernoulli $Γ$-action) is cocycle superrigid. If in addition $H'$ can be taken non-virtually abelian and $Γ\curvearrowright X$ is an arbitrary free ergodic action while $Λ\curvearrowright Y=\Bbb T^Λ$ is a Bernoulli action of an arbitrary infinite conjugacy class group, then any isomorphism of the associated II$_1$ factors $L^\infty X \rtimes Γ\simeq L^\infty Y \rtimes Λ$ comes from a conjugacy of the actions.Final version; paper appeared in Journal of the Amer. Math. Soc., 2007Group TheoryOperator Algebras28D15, 46L10, 46L35, 20E05text