勷勤数学•专家报告

题      目：Flag-transitive 2-designs with prime-square or prime-cube block length

报  告  人：周胜林 教授  (邀请人：袁平之)

                                             华南理工大学       

时      间：4月11日  15：30-16：30

地     点：数科院东楼401报告厅

报告人简介:

        周胜林，华南理工大学数学学院教授，博士生导师。主要从事代数学、群与组合设计等领域的教学和研究工作，已发表SCI论文100余篇，主持过国家、省部级项目多项。

摘      要：

     We study $2$-$(v,k,\lambda)$ designs $\mathcal D=(\mathcal P,\mathcal B)$ 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 $G \leq H\wr S_2$ acting on ${\mathcal P}=\Delta \times \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 $\mu$ is the size of the nonempty set $B\cap C$ with $B\in \mathcal B$ 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.

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