  Let $\pi_1(C)$ be the algebraic fundamental group of a smooth connected
affine curve, defined over an algebraically closed field of characteristic
$p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic)
subgroup of $\pi_1(C)$. Under the hypothesis that the quotient $\pi_1(C)/N$
admits an infinitely generated Sylow $p$-subgroup, we prove that $N$ is indeed
isomorphic to a normal (resp. characteristic) subgroup of a free profinite
group of countable cardinality. As a consequence, every proper open subgroup of
$N$ is a free profinite group of countable cardinality.
