Solvable Block-Transitive Automorphism Groups of 2−(v, k, 1) Designs

Let k⩾3 be a fixed positive integer and (G, D) be a pair, where D is a 2−(v, k, 1) design and G is a group of automorphisms of D such that G is solvable and block-transitive on D. If v>(k3/4+1)ϕ(k(k−1)), then v is a power of a prime number p and G is flag-transitive or G⩽AΓL(1, v).