Classification of point-primitive linear spaces with

2pq points∗

Haiyan Guan  Shenglin Zhou

Abstract

This paper is a further contribution to the classification of point-primitive finite linear spaces. Let p,q be two primes. We prove that if S is a non-trivial finite linear space with 2pq points, and G ≤ Aut (S) is point-primitive, then G is line-transitive and S is the Ree unital U R ( 3 ) , or the Hermitian unital U H ( s ) .