Affine groups as flag-transitive and point-primitive automorphism groups of symmetric designs

In this article, we investigate symmetric designs admitting flag-transitive and point-primitive affine automorphism groups. We prove that if a flag-transitive automorphism group G of a symmetric (v, k, ?) design with ? prime is point-primitive of affine type, then G = 26:S6 and (v, k,?) = (16, 6, 2), or G is a subgroup of A Gamma L1(q) for some odd prime power q. In conclusion, we present a classification of flag-transitive and point-primitive symmetric designs with ? prime, which says that such an incidence structure is a projective space PG(n, q), it has parameter set (15, 7, 3), (7, 4, 2), (11, 5, 2), (11, 6, 2), (16, 6, 2) or (45, 12, 3), or v = pd where pis an odd prime and the automorphism group is a subgroup of A Gamma L1(q).