Embedding problems for subgroups of the fundamental group

Abstract

Let ${\pi }_1(C)$ be the fundamental group of a smooth irreducible affine curve $C$ over an algebraically closed field of positive characteristic. It is shown that given an embedding problem for ${\pi }_1(C)$ there exist an open index $p$ normal subgroup of ${\pi }_1(C)$ so that the embedding problem restricted to this group has a solution. In particular, ${\pi }_1(C)$ is "almost $\omega$-free".

WithDrawn. Incomplete