Innovations in Incidence Geometry

Projective planes with a transitive automorphism group

Alan R. Camina

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In this note we prove two theorems which contribute towards the classification of line-transitive designs. A special class of such designs are the projective planes and it is this problem which the paper addresses. There two main results:-

Theorem A: Let G act line-transitively on a projective plane P and let M be a minimal normal subgroup of G. Then M is either abelian or simple or the order of the plane is 3,9,16 or 25.

Theorem B: Let G be a classical simple group which acts line-transitively on a projective plane. Then the rank of G is bounded.

Article information

Innov. Incidence Geom., Volume 1, Number 1 (2005), 191-196.

Received: 27 August 2004
Accepted: 4 March 2005
First available in Project Euclid: 26 February 2019

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 51A35: Non-Desarguesian affine and projective planes
Secondary: 20B25: Finite automorphism groups of algebraic, geometric, or combinatorial structures [See also 05Bxx, 12F10, 20G40, 20H30, 51-XX]

projective planes simple groups


Camina, Alan R. Projective planes with a transitive automorphism group. Innov. Incidence Geom. 1 (2005), no. 1, 191--196. doi:10.2140/iig.2005.1.191.

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