On Flag-Transitive Symmetric Designs of Affine Type

It is shown that, if D is a nontrivial 2-(v, k, lambda) symmetric design, with (k, lambda) = 1, admitting a flag-transitive automorphism group G of affine type, then v = p(d), p an odd prime, and G is a point-primitive, block-primitive subgroup of A Gamma L-1(p(d)). Moreover, O(G) acts flag-transitively, point-primitively on D, and D is isomorphic to the development of a difference set whose parameters and structure are also provided.(C) 2016 Wiley Periodicals, Inc.