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

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

2009-07-07

arxiv.org/abs/0907.1281v1

Mathematics

Combinatorics

5 pages; to appear in: "Journal of Combinatorial Theory, Series A"

Scientific paper

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 $n>2$.

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