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 $\mathrm{PSL}(n,q)$ for some $n\ge 3$. 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 $\mathrm{PG}(n-1,3)$ as input to this construction yields a G-flag-transitive 2-$(v,3,2)$ design where G has socle $\mathrm{PSL}(n,3)$ and $v=(3^n-1)/2$. Apart from these designs, our classification yields exactly one other example, namely the complement of the Fano plane.

本文致力于标志传递2-的分类$（v，ķ，2）$设计。我们表明，除了两个已知的对称2-$（16，6，2）$设计中，一个非平凡2-自同构群的每个标志传递子群G$（v，ķ，2）$设计是原始的仿射或几乎简单的类型。此外，我们将2-$（v，ķ，2）$设计允许带有底的标志传递近乎简单的G组$\mathrm{PSL}（ñ，q）$ 对于一些 $ñ\ge 3$。除此分析外，我们还给出了标记可传递2的构造$（v，ķ-\mathrm{1个}，ķ-2）$ 从给定的标记传递2进行设计$（v，ķ，\mathrm{1个}）$设计可以在线路上引起2个传递动作。进行投影空间的点和线的设计$\mathrm{PG}（ñ-\mathrm{1个}，3）$作为此构造的输入会产生G标志传递2$（v，3，2）$G有鞋底的设计$\mathrm{PSL}（ñ，3）$ 和 $v=（3^{ñ}-\mathrm{1个}）/2$。除了这些设计之外，我们的分类还提供了另一个示例，即Fano平面的补码。