  We prove that for any closed Lorentz $4$-manifold $(M,g)$ the isometry group
$Isom(M,g)$ is Jordan. Namely, there exists a constant $C$ (depending on $M$
and $g$) such that any finite subgroup $\Gamma\leq Isom(M,g)$ has an abelian
subgroup $A\leq\Gamma$ satisfying $[\Gamma:A]\leq C$.
