  The goal of this paper is to obtain restrictions on the prime to p quotient
of the \'etale fundamental group of a smooth projective variety in
characteristic $p\ge 0$. The results are analogues some theorems in the study
of K\"ahler groups. Our first main result is that such groups are
indecomposable under coproduct. The second gives a classification of the
pro-$\ell$ parts of one relator groups in this class.
