Abstract

We construct a rank $3$ geometry $\Gamma \left(O^{\prime }N\right)$ over the diagram whose automorphism group is the O’Nan sporadic simple group. The maximal parabolic subgroups are the Janko group $J_1$, $2\times S_5$ and the Mathieu group $M_{11}$. Our construction is based on a convenient amalgam of known geometries of rank $2$ for $J_1$ and $M_{11}$ extracted from the subgroup lattice of $O^{\prime }N$.

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Mathematical Subject Classification 2010

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