Finite linear spaces admitting a two-dimensional projective linear group

This article is a contribution to the study of linear spaces admitting a line-transitive automorphism group. We classify such linear spaces where PSL(2,q), q>3 acts line transitively. We prove that the only cases which arise are projective planes, a Bose–Witt–Shrikhande linear space and one more space admitting PSL(2,26) as a line-transitive automorphism group.