论文标题
在国旗传输上$ 2 $ - $（k^{2}，k，λ）$设计，$λ\ mid k $
On Flag-Transitive $2$-$(k^{2}, k, λ)$ Designs with $λ\mid k$
论文作者
论文摘要
结果表明，除了最小的REE集团之外，一个$ 2 $ - $ - $ - $（k^{2}，k，λ）$ Design D，带有$λ\ mid k $的$ 2 $ - $ - $ g $的自动形态$ g $是一个亲戚组或几乎简单的古典组。此外，当$ g $是最小的REE组时，$ \ Mathcal {d} $是同构成$ 2 $ - $（62、6、2）$ design，或者是本文中构建的三个$ 2 $ - $ - $ - $ - $ - $（62、6、6）$的设计。所有的四个$ 2 $ -DESIGNS都将$ 36 $的固定量的$ 36 $ SEVENT的$ \ MATHCAL {C} $ $ PG_ {2}（8）$作为点集，而6个集合中的6组sests作为块集。
It is shown that, apart from the smallest Ree group, a flag-transitive automorphism group $G$ of a $2$-$(k^{2}, k, λ)$ design D, with $λ\mid k$, is either an affine group or an almost simple classical group. Moreover, when $G$ is the smallest Ree group, $\mathcal{D}$ is isomorphic either to the $2$-$(62, 6, 2)$ design or to one of the three $2$- $(62, 6, 6)$ designs constructed in this paper. All the four $2$-designs have the $36$ secants of a nondegenerate conic $\mathcal{C}$ of $PG_{2}(8)$ as a point set and 6-sets of secants in a remarkable configuration as a block set.
