论文标题
多重传递性除了不可侵犯的系统
Multiple transitivity except for a system of imprimitivity
论文作者
论文摘要
令$ω$为配备等价关系$ \ sim $的集合；我们将等价类称为$ω$的块。 A permutation group $G \le \mathrm{Sym}(Ω)$ is $k$-by-block-transitive if $\sim$ is $G$-invariant, with at least $k$ blocks, and $G$ is transitive on the set of $k$-tuples of points such that no two entries lie in the same block.如果对块的行动是忠实的，则该行动是封锁的。在本文中，我们将有限的Block-Faithful $ 2 $ by-by-by-by-by-by-by-by-by-bys-block-thembock-thembock-thembock Fransitive Actions进行了分类。我们还表明，对于$ k \ ge 3 $，没有有限的块 - 信仰$ k $ by-by-by-by-bytentive take blovial Blocks。
Let $Ω$ be a set equipped with an equivalence relation $\sim$; we refer to the equivalence classes as blocks of $Ω$. A permutation group $G \le \mathrm{Sym}(Ω)$ is $k$-by-block-transitive if $\sim$ is $G$-invariant, with at least $k$ blocks, and $G$ is transitive on the set of $k$-tuples of points such that no two entries lie in the same block. The action is block-faithful if the action on the set of blocks is faithful. In this article we classify the finite block-faithful $2$-by-block-transitive actions. We also show that for $k \ge 3$, there are no finite block-faithful $k$-by-block-transitive actions with nontrivial blocks.
