Flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1 and alternating socle

Consider the flag-transitive 2-(v, k, λ) symmetric designs with (k, λ) = 1.We prove that if D is a nontrivial 2-(v, k, λ) symmetric design with (k, λ) = 1 and G ≤ Aut(D) is flag-transitive with Soc(G) = An for n ≥ 5, then D is the projective space PG2(3, 2) and G = A7.

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