论文标题
通过Cayley图表的自动形态组的因子图
Factor maps for automorphism groups via Cayley diagrams
论文作者
论文摘要
我们通过两种方式利用小组动作和边缘标记图之间的对应关系。首先，我们给出了几个民间传说结果的统一介绍，该结果将弱遏制，局部全球收敛和连续模型理论联系起来。其次，我们研究了$ \ operatorname {aut}（\ operatorname {cay}（γ））$ - fiid Comminatorics和$γ$ -FIID组合物的各种标记组$γ$。直接看到，当$ \ operatorname {cay}（γ）$允许$ \ permatatorName {aut}（\ propatatorName {cay}（cay}（γ））$ - fiid cayley Daugram时，这些差异就消失了。我们将其扩展为表明，当$ \ operatorname {cay}（γ）$接受近似的fiid fiid cayley图时，近似组合的组合是相同的，我们给出了几个cayley图形（近似）fiid cayley fiid cayley cayley图的组的示例和非示例。 特别是，我们表明树木允许任何cayley图是一棵树的群体的大约Cayley图。无扭转的cayley图形nilpotent组不接受fiid cayley图；并且有一些具有同构cayley图的组，因此只有一个人甚至可以承认近似的cayley图（实际上，我们的构造回答了Weilacher的问题）。
We leverage a correspondence between group actions and edge-labelled graphs in two ways. First, we give a unified presentation of several folklore results connecting weak containment, local-global convergence, and continuous model theory. Second, we investigate the difference between $\operatorname{Aut}(\operatorname{Cay}(Γ))$-fiid combinatorics and $Γ$-fiid combinatorics for various marked groups $Γ$. It's straightforward to see that these differences vanish when $\operatorname{Cay}(Γ)$ admits an $\operatorname{Aut}(\operatorname{Cay}(Γ))$-fiid Cayley diagram. We extend this to show that the approximate combinatorics are the same when $\operatorname{Cay}(Γ)$ admits an approximate fiid Cayley diagram, and we give several examples and nonexamples of groups whose Cayley graphs admit (approximate) fiid Cayley diagrams. In particular, we show that trees admit approximate Cayley diagrams for any group whose Cayley graph is a tree; Cayley graphs of torsion free nilpotent groups do not admit fiid Cayley diagrams; and there are groups with isomorphic Cayley graphs so that only one them admits even an approximate Cayley diagram (in fact our construction answers a question of Weilacher).
