On Jordan type bounds for finite groups acting on compact 3-manifolds

By a classical result of Jordan each finite subgroup of a complex linear group GL_n(C) has an abelian normal subgroup whose index is bounded by a constant depending only on n. It has been asked whether this remains true for finite subgroups of the diffeomorphism group Diff(M) of every compact manifold M; in the present paper, using the geometrization of 3-manifolds, we prove it for compact 3-manifolds M.