#### Vol. 6+7, No. 1, 2008

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A note on the group of projectivities of finite planes

### Peter Müller and Gábor Péter Nagy

Vol. 6+7 (2008), No. 1, 291–294
DOI: 10.2140/iig.2008.6.291
##### 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 ${\mathsf{S}}_{n+1}$.

##### Keywords
projective planes, projectivities, loops
##### Mathematical Subject Classification 2000
Primary: 20N05, 51E15