A note on integrability and finite orbits for subgroups of Diff(C^n,0)

In this note we extend to arbitrary dimensions a couple of results due respectively to Mattei-Moussu and to Camara-Scardua in dimension 2. We also provide examples of singular foliations having a Siegel-type singularity and answering in the negative the central question left open in the previous work of Camara-Scardua.