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

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 M24. 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 An+1 or to the symmetric group Sn+1.

projective planes, projectivities, loops
Mathematical Subject Classification 2000
Primary: 20N05, 51E15
Received: 21 February 2008
Accepted: 7 March 2008
Peter Müller
Gábor Péter Nagy