  Let $N=L_n(q)$, {$n \geq 2$}, $q$ a prime power, be a projective linear
simple group. We classify all Steiner quadruple systems admitting a group $G$
with $N \leq G \leq \Aut(N)$. In particular, we show that $G$ cannot act as a
group of automorphisms on any Steiner quadruple system for $n>2$.
