论文标题
在树木上采用规定的地方行动的小组
Groups Acting on Trees With Prescribed Local Action
论文作者
论文摘要
我们扩展了汉堡的封闭式，非杂物，局部准求的自动形态群体的理论，这些自动形态是局部有限的，连接的图表到半偶然案例的，并发展了汉堡的概括 - 跨性别群体，该集团在\ in \ in \ in \ in \ in \ nte p_ in \ in \ mathbb {n n and} n} n} $ d f \ in \ in} $ d f。给出了三个应用程序：首先，我们表征了$ \ mathrm {aut}（t_ {d}）$的非污染子组的准中心类型的自动形态类型。在此过程中，我们用非平凡的准中心明确构建了$ \ mathrm {aut}（t_ {d}）$的$ \ mathrm {aut}（t_ {d}）$的封闭的，紧凑的子组，并看到汉堡理论并未进一步扩展到瞬时情况。然后，我们表征$（p_ {k}）$ - $ \ mathrm {aut}（t_ {d}）$包含涉及反转的本地传递子组的关闭，从而部分回答了银行的两个问题 - elder-willis。最后，我们提供了有关魏斯猜想的新观点。
We extend Burger--Mozes theory of closed, non-discrete, locally quasiprimitive automorphism groups of locally finite, connected graphs to the semiprimitive case, and develop a generalization of Burger--Mozes universal groups acting on the regular tree $T_{d}$ of degree $d\in\mathbb{N}_{\ge 3}$. Three applications are given: First, we characterize the automorphism types which the quasi-center of a non-discrete subgroup of $\mathrm{Aut}(T_{d})$ may feature in terms of the group's local~action. In doing so, we explicitly construct closed, non-discrete, compactly generated subgroups of $\mathrm{Aut}(T_{d})$ with non-trivial quasi-center, and see that Burger--Mozes theory does not extend further to the transitive case. We then characterize the $(P_{k})$-closures of locally transitive subgroups of $\mathrm{Aut}(T_{d})$ containing an involutive inversion, and thereby partially answer two questions by Banks--Elder--Willis. Finally, we offer a new view on the Weiss conjecture.
