Block‐Transitive Automorphism Groups of 2‐(v,5,λ) Designs

ABSTRACT This paper investigates 2‐ designs admitting a block‐transitive automorphism group . We first prove that if is point‐imprimitive, then must be one of 16, 21, or 81. We further provide a complete classification of all such designs for and . Second, we demonstrate that if is point‐primitive, then it must be of affine type, almost simple type, or product type. Additionally, we present a classification of pairs where is of product type.