Calcul du groupe de Galois du produit de trois opérateurs différentiels complètement réductibles

In this Note, we give a complete description of the unipotent radical of the differential Galois group of an operator of the form LXLALY where LX,LA,LY are completely reducible. We start with the case where this group has an Abelian unipotent radical; we then show how one can reduce the general case to the above case. To cite this article: C. Hardouin, C. R. Acad. Sci. Paris, Ser. I 341 (2005).