Innovations in Incidence Geometry
- Innov. Incidence Geom.
- Volume 1, Number 1 (2005), 191-196.
Projective planes with a transitive automorphism group
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 act line-transitively on a projective plane and let be a minimal normal subgroup of . Then is either abelian or simple or the order of the plane is or .
Theorem B: Let be a classical simple group which acts line-transitively on a projective plane. Then the rank of is bounded.
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
Permanent link to this document
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]
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. https://projecteuclid.org/euclid.iig/1551206821