AI 中文总结
研究有限生成的收缩自相似分支群的可公度作用并分类，通过建立迭代单值群的FW性质给出无限有限生成顺从群的首个例子，还证明收缩自相似正则分支群不具PW性质，如首个格里戈丘克群。
AI 中文摘要
可公度作用控制着一个群如何作用于CAT(0)立方体复形。我们对每个有限生成的收缩自相似分支群进行了分类。作为主要应用，我们为生成经典正方形谢尔宾斯基地毯的细分规则的迭代单值群建立了FW性质。这是具有FW性质的无限有限生成顺从群的首个例子，回答了Cornulier的一个问题。另一个应用是，我们证明收缩自相似正则分支群不具有PW性质。特别是，第一个格里戈丘克群不具有PW性质，回答了文献中的另一个问题。
英文摘要
Commensurating actions govern how a group can act on non-positively curved cube complexes. We obtain a complete picture of them for a class of finitely generated groups acting on rooted trees: contracting self-similar branch groups. The main application is a proof of Property FW for the iterated monodromy group of the subdivision rule generating the classical square Sierpiński carpet. This is the first example of an infinite finitely generated amenable group with Property FW, answering a question of Cornulier. As another application, we show that a contracting self-similar regular branch group does not have Property PW. In particular, the Grigorchuk group does not have Property PW, answering another question in the literature.
Comments34 pages, 3 figures. v2: minor revision
