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 $\mathcal{P}$ 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

Mathematical Subject Classification 2000

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