On flag-transitive automorphism groups of 2-designs

作者：Zhong, Chuyi; Zhou, Shenglin^*

来源：Discrete Mathematics, 2023, 346(2): 113227.

DOI：10.1016/j.disc.2022.113227

• 2-design
• Automorphism group
• Point-primitive
• Flag-transitive

In this paper, we study flag-transitive 2-designs. Let D be a 2-(v, k, A) design with (v - 1, k - 1) < (v -1)12 admitting a flag-transitive automorphism group G. We prove that G is of affine, almost simple type, or product type with rank(G) = 3. In particular, if (v -1, k - 1) = 3 or 4, then G is of affine, almost simple type except the case that Soc(G) = A5 x A5 and D is a 2-(25, 4, 12) or 2-(25, 4, 18) design. Finally, an application to the case where k is prime is also discussed.