论文标题
在国旗传输2-（v，k，2）设计上
On flag-transitive 2-(v,k,2) designs
论文作者
论文摘要
本文致力于对标志传输2-（v，k，2）设计的分类。我们表明，除了两个已知的对称2-（16,6,2）设计外，非平凡2-（v，k，2）设计的每个旗帜传输子组G是仿射或几乎简单类型的原始设计。此外，我们对2-（v，k，2）的设计进行分类，该设计对一些n \ geq 3进行了旗帜传递的几乎简单的组G。以射影空间PG（N-1,3）为输入的点和线的设计产生了G-FLAG传播的2-（V，3,2）设计，其中G具有SOCLE PSL（n，3）和V =（3^n-1）/2。除了这些设计外，我们的PSL分类完全产生了另一个例子，即Fano平面的补充。
This paper is devoted to the classification of flag-transitive 2-(v,k,2) designs. We show that apart from two known symmetric 2-(16,6,2) designs, every flag-transitive subgroup G of the automorphism group of a nontrivial 2-(v,k,2) design is primitive of affine or almost simple type. Moreover, we classify the 2-(v,k,2) designs admitting a flag transitive almost simple group G with socle PSL(n,q) for some n \geq 3. Alongside this analysis, we give a construction for a flag-transitive 2-(v,k-1,k-2) design from a given flag-transitive 2-(v,k,1) design which induces a 2-transitive action on a line. Taking the design of points and lines of the projective space PG(n-1,3) as input to this construction yields a G-flag-transitive 2-(v,3,2) design where G has socle PSL(n,3) and v=(3^n-1)/2. Apart from these designs, our PSL-classification yields exactly one other example, namely the complement of the Fano plane.
