  Let $k$ be an algebraically closed field of characteristic $p>0$ and let
$C/k$ be a smooth connected affine curve. Denote by $\pi_1(C)$ its algebraic
fundamental group. The goal of this paper is to characterize a certain subset
of closed normal subgroups $N$ of $\pi_1(C)$. In "Normal subgroups of
fundamental groups of affine curves in positive characteristic" we proved the
same result under the additional hypothesis that $k$ had countable cardinality.
