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

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.

projective planes, simple groups
Mathematical Subject Classification 2000
Primary: 51A35
Secondary: 20B25
Received: 27 August 2004
Accepted: 4 March 2005
Alan Robert Camina