Infinite geometric groups of rank 4
A permutation group \(G\) is geometric if the pointwise stabilizer of any finite sequence of points acts transitively on the set of points it does not fix (if there are any). If there is \(r \in \mathbb{N}\) such that the stabiliser of some \(r\) points is the identity, then \(r\) is called the rank of \(G\). The group \(G\) has finite type if it has finite rank and the stabiliser of any sequence of length less than \(r\) has just finitely many fixed points. The author gives here a very short geometric proof that there is no infinite geometric group of finite rank at least 4 and finite type.
scientific article; zbMATH DE number 64835