  We study groups of formal diffeomorphisms in several complex variables. For
abelian, metabelian or nilpotent groups we investigate the existence of
suitable formal vector fields and closed differential forms which exhibit an
invariance property under the group action. Our results are applicable in the
construction of suitable integrating factors for holomorphic foliations with
singularities. We believe they are a starting point in the study of the
connection between Liouvillian integration and transverse structures of
holomorphic foliations with singularities in the case of arbitrary codimension.
