#### Vol. 1, No. 1, 2005

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Projective planes with a transitive automorphism group

### Alan Robert Camina

Vol. 1 (2005), No. 1, 191–196
##### 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 $\mathsc{P}$ 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.

##### Keywords
projective planes, simple groups
Primary: 51A35
Secondary: 20B25