论文标题
块传输$ 3 $ - $（v，k，1）$设计与交替组相关
Block-transitive $3$-$(v,k,1)$ designs associated with alternating groups
论文作者
论文摘要
令$ \ Mathcal {d} $为非平凡的$ 3 $ - $（V，K，1）$设计，允许块变量$ g $ g $自动形态。 Gan和第二作者的最新作品断言，$ G $是仿射或几乎简单的。在本文中，证明，如果$ g $与Socle交替组几乎很简单，那么$ \ Mathcal {d} $是唯一的$ 3 $ - $ - $（10,4,1）$设计，$ g = \ g = \ mathrm {pgl}（pgl}（2,9）（2,9） $ \ MATHRM {aut}（\ Mathrm {a} _6）= \ Mathrm {S} _6：\ Mathrm {z} _2 $，而$ G $是flag-transistive。
Let $\mathcal{D}$ be a nontrivial $3$-$(v,k,1)$ design admitting a block-transitive group $G$ of automorphisms. A recent work of Gan and the second author asserts that $G$ is either affine or almost simple. In this paper, it is proved that if $G$ is almost simple with socle an alternating group, then $\mathcal{D}$ is the unique $3$-$(10,4,1)$ design, and $G=\mathrm{PGL}(2,9)$, $\mathrm{M}_{10}$ or $\mathrm{Aut}(\mathrm{A}_6 )=\mathrm{S}_6:\mathrm{Z}_2$, and $G$ is flag-transitive.
