  We study groups of germs of complex diffeomorphisms having a property called
irreducibility. The notion is motivated by a similar property of the
fundamental group of the complement of an irreducible hypersurface in the
complex projective space. Natural examples of such groups of germ maps are
given by holonomy groups and monodromy groups of integrable systems
(foliations) under certain conditions on the singular or ramification set. The
case of complex dimension one is studied in [7] where finiteness is proved for
irreducible groups under certain arithmetic hypothesis on the linear part. In
dimension $n \geq 2$ the picture changes since linear groups are not always
abelian in dimension two or bigger. Nevertheless, we still obtain a finiteness
result under some conditions in the linear part of the group, for instance if
the linear part is abelian. Examples are given illustrating the role of our
hypotheses. Applications are given to the framework of holomorphic foliations
and analytic deformations of rational fibrations by Riccati foliations.
