Finite linear spaces admitting a projective group PSU(3, q) with q even

Abstract

This article is a contribution to the study of the automorphism groups of finite linear spaces. In particular we look at simple groups and prove the following theorem: Let G=PSU(3, q) with q even and G acts line-transitively on a finite linear space S . Then S is one of the following cases: (i) A projective plane; (ii) A regular linear space with parameters ( b, v, r, k)=( q 2( q 2− q+1), q 3+1, q 2− q+1, q+1). This is called the Hermitian unitary design.