Flag-Transitive 2-v,5,λ Designs Admitting a Two-Dimensional Projective Group

Abstract

The focus of this study is to classify flag-transitive 2-designs. We have come to the conclusion that if D is a nontrivial 2-design having block size 5 and G is a two-dimensional projective special linear group which acts flag-transitively on D with q≢1 (mod 4), then D is a 2-(11, 5, 2) design, a 2-(11, 5, 12) design, a 2-q+1,5,2q−1 design with q≡3 (mod 4) or a 2-q+1,5,q−1/3 design with q=2f (where f>2 is an even).