Abstract

In this short note we show that the group of projectivities of a projective plane of order $23$ cannot be isomorphic to the Mathieu group ${\mathsf{M}}_{24}$. By a result of T. Grundhöfer, this implies that the group of projectivities of a non-desarguesian projective plane of finite order $n$ is isomorphic either to the alternating group ${\mathsf{A}}_{n+1}$ or to the symmetric group ${\mathsf{S}}_{n+1}$.

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Mathematical Subject Classification 2000

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