组合数学系列报告——Flag-transitive 2-designs with prime-square or prime-cube block length

报告人：周胜林（华南理工大学）

时间：2025年3月7日,11:00-12:00

地点：海纳苑2幢820室

摘要：We study 2-(v,k, lambda) designs  D=(P, B) admitting a flag-transitive automorphism group G,  where k=p^2 or p^3, and p is prime. We prove that if k=p^2, then G must be point-primitive, and G is of affine or almost simple type except for two examples. If k=p^3, and G is point-primitive, then G is of affine, almost simple, or product type with G<= H wr S_2 acting on P= Delta X Delta , where H is a primitive group on Delta. Furthermore, if G is point-imprimitive with a system Sigma of imprimitivity consisting of d classes of size c, we determine the parameters (v,k, mu,c,d), where mu=|b cap C| with b in B and C in Sigma. Moreover, some infinite families of flag-transitive 2-(v,p^3, lambda) designs are also constructed. This is a joint work with Dr. Chuyi Zhong.

联系人：冯涛（tfeng@zju.edu.cn）