Flag-transitive, point-imprimitive symmetric 2-(v, k, λ) designs with k > λ (λ-3) /2

Let D = (P, B) be a symmetric 2-(v, k, lambda) design admitting a flag-transitive, point imprimitive automorphism group G that leaves invariant a non-trivial partition Sigma of P. Praeger and Zhou [42] have shown that, there is a constant k(0) such that, for each B is an element of B and Delta is an element of Sigma, the size of |B boolean AND Delta| is either 0 or k(0). In the present paper we show that, if k > lambda (lambda - 3) /2 and k(0) >= 3, D is isomorphic to one of the known flag-transitive, poin-timprimitive symmetric 2-designs with parameters (45, 12, 3) or (96, 20, 4). (c) 2024 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons .org /licenses /by /4 .0/).