Flag-transitive 2-(v, k, ?) designs with ? prime and alternating socle

摘要

This paper is a contribution to the classification of 2-designs admitting a flag-transitive automorphism group. Let D be a 2-(v, k, lambda) design with lambda prime and G be a flag-transitive, point-primitive automorphism group of D. We prove that if the socle of G is an alternating group, then D has parameters (v, k, lambda) = (15, 7, 3), (6,3, 2), (10, 6,5) or (10, 4, 2).

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