论文标题
在有限的最大顶点稳定器上作用在树木上的Pro-P组，直到结合
Pro-p groups acting on trees with finitely many maximal vertex stabilizers up to conjugation
论文作者
论文摘要
我们证明，有限生成的Pro-P $组$ g $在Pro-P $ p $ p $ t $ t $ splitts上作为免费的合并Pro-P $ puds或Pro-P $ p $ hnn-Extension上的Edge稳定器上的extension。如果$ g $具有有限的许多顶点稳定器，以达到共轭，我们表明，这是Pro-P $组$（\ cal G，γ）的有限图的基本pro-P $组，具有Edge and vertex组，是稳定器的某些角度和边缘的稳定器。如果边缘稳定器是procyclic，我们就$ g $的发电机数量最少，对$γ$进行限制。我们还提供了一个pro-$ p $组$ g $的标准，以便根据第一个同胞$ h^1（g，\ mathbb {f} _p [[g]]）$访问。
We prove that a finitely generated pro-$p$ group $G$ acting on a pro-$p$ tree $T$ splits as a free amalgamated pro-$p$ product or a pro-$p$ HNN-extension over an edge stabilizer. If $G$ acts with finitely many vertex stabilizers up to conjugation we show that it is the fundamental pro-$p$ group of a finite graph of pro-$p$ groups $(\cal G, Γ)$ with edge and vertex groups being stabilizers of certain vertices and edges of $T$ respectively. If edge stabilizers are procyclic, we give a bound on $Γ$ in terms of the minimal number of generators of $G$. We also give a criterion for a pro-$p$ group $G$ to be accessible in terms of the first cohomology $H^1(G, \mathbb{F}_p[[G]])$.
