  Let X be a smooth projective algebraic curve of genus g minus $r\geq 1$
points defined over an algebraically closed field k of characteristic $p\geq
0$. The structure of the largest prime to p quotient of the \'etale fundamental
group is well known by transcendental methods : it is isomorphic to the largest
prime to p quotient of a free pro-finite group on 2g+r-1 generators. We show
that, with purely algebraic means, we can prove the corresponding result for
the largest pro-solvable quotient of these groups.
