Block-Transitive Symmetric Designs and Alternating Groups

摘要

This paper studies symmetric (v, k, ?) designs D with v odd and admitting a block-transitive automorphism group G whose socle is an alternating group A(n). We indeed show that for given ?, only finitely many such designs exist and prove that if 2 = ? = 5, then D = PG(2)(3, 2) or its complement and G = S-5, S-6, A(n) (n = 5, 6, 7, 8).

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