  A century ago, Camille Jordan proved that the complex general linear group
$GL_n(C)$ has the Jordan property: there is a Jordan constant $C_n$ such that
every finite subgroup $H \le GL_n(C)$ has an abelian subgroup $H_1$ of index
$[H : H_1] \le C_n$. We show that every connected algebraic group $G$ (which is
not necessarily linear) has the Jordan property with the Jordan constant
depending only on $\dim \, G$, and that the full automorphism group $Aut(X)$ of
every projective variety $X$ has the Jordan property
