Derived length of solvable groups of local diffeomorphisms

Abstract

Let $G$ be a solvable subgroup of the group $\diff{}{n}$ of local complex analytic diffeomorphisms. Analogously as for groups of matrices we bound the solvable length of $G$ by a function of $n$. Moreover we provide the best possible bounds for connected, unipotent and nilpotent groups.

27 pages