Block-Transitive Symmetric Designs and Alternating Groups

作者：Zhang, Xiaohong^*; Zhou, Shenglin

来源：Results in Mathematics, 2023, 78(5): 185.

DOI：10.1007/s00025-023-01964-w

• Symmetric design
• block-transitive
• alternating socle
• automorphism
• fixed points

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).