  Let $G$ be a group with socle a simple group of Lie type defined over the
finite field with $q$ elements where $q$ is a power of the prime $p$. Suppose
that $G$ acts transitively upon the lines of a linear space $\mathcal{S}$. We
show that if $p$ is {\it significant} then $G$ acts flag-transitively on
$\mathcal{S}$ and all examples are known.
