Juan J. Morales-Ruiz and David B. Sanz - 
"Local and global properties of Lie-Vessiot systems".

We explore a classical Lie's result on the superposition of
solutions for ordinary differential equations. This theorem
characterizes locally the class of differential equations 
admitting superposition laws. We introduce the notion 
of pretransitive Lie-Vessiot system, wich form the
class of equations admitting global superposition laws. We
develop a differential Galois theory for these equations, and
study their reduction and integration.