## Innovations in Incidence Geometry

### Projective planes with a transitive automorphism group

Alan R. Camina

#### Abstract

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

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

Dates
Accepted: 4 March 2005
First available in Project Euclid: 26 February 2019

https://projecteuclid.org/euclid.iig/1551206821

Digital Object Identifier
doi:10.2140/iig.2005.1.191

Mathematical Reviews number (MathSciNet)
MR2213959

Zentralblatt MATH identifier
1099.51004

Keywords
projective planes simple groups

#### Citation

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

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