Innovations in Incidence Geometry

A note on the group of projectivities of finite projective planes

Peter Müller and Gábor P. Nagy

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Abstract

In this short note we show that the group of projectivities of a projective plane of order 2 3 cannot be isomorphic to the Mathieu group M 2 4 . 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 A n + 1 or to the symmetric group S n + 1 .

Article information

Source
Innov. Incidence Geom., Volume 6-7, Number 1 (2007), 291-294.

Dates
Received: 21 February 2008
Accepted: 7 March 2008
First available in Project Euclid: 28 February 2019

Permanent link to this document
https://projecteuclid.org/euclid.iig/1551323184

Digital Object Identifier
doi:10.2140/iig.2008.6.291

Mathematical Reviews number (MathSciNet)
MR2515272

Zentralblatt MATH identifier
1172.51007

Subjects
Primary: 20N05: Loops, quasigroups [See also 05Bxx] 51E15: Affine and projective planes

Keywords
projective planes projectivities loops

Citation

Müller, Peter; Nagy, Gábor P. A note on the group of projectivities of finite projective planes. Innov. Incidence Geom. 6-7 (2007), no. 1, 291--294. doi:10.2140/iig.2008.6.291. https://projecteuclid.org/euclid.iig/1551323184


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