SAG II: Singularities, holomorphic foliations, and complex geometry

The soluble length of a solvable matrix group in GL(n,C) is bounded by (n) where is the Newman function. It is interesting to study the analogous problem for solvable groups of germs of diffeomorphisms because of the implications in the study of integrability of holomorphic foliations. We provide estimates for the soluble length in terms of the dimension. Moreover we optain the optimal estimates for nilpotent, unipotent and connected groups. This is a joint work with Mitchel Alfonso.