Transitive projective planes and insoluble groups

Abstract

Suppose that a group $G$ acts transitively on the points of $\mathcal{P}$, a finite non-Desarguesian projective plane. We prove that if $G$ is insoluble then $G/O(G)$ is isomorphic to $S{L}_2(5)$ or $S{L}_2(5).2$.

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