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Let $N=L_n(q)$, {$n \geq 2$}, $q$ a prime power, be a projective linearsimple 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 agroup of automorphisms on any Steiner quadruple system for $n>2$.

Almost simple groups with socle $L_n(q)$ acting on Steiner quadruple systems