Formal Invariants for Nonsolvable Subgroups of Diffω( , 0)

Let G be a nonsolvable subgroup of Diffω( , 0). We derive an infinite sequence of additive subgroups Gk , k , depending only on the conjugacy class of G within Diffω( , 0). As an application, we prove that G is conjugate within Diffω( , 0) to a subgroup of Diffω( , 0) if and only if all Gk are real.