Infinite geometric groups of rank 4
type: Item
instance of: scholarly article
title: Infinite geometric groups of rank 4
zbMATH Open document ID: 0808.20005
DOI: 10.1016/0195-6698(92)90040-7
author: Peter J. Cameron
published in: European Journal of Combinatorics
publication date: 1992-09-27T00:00:00Z
review text: 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.
reviewed by: H. D. Macpherson
Mathematics Subject Classification ID: 20B22
Mathematics Subject Classification ID: 20F65
zbMATH DE Number: 64835
zbMATH Keywords: geometric permutation group
zbMATH Keywords: pointwise stabilizer
zbMATH Keywords: finite type
zbMATH Keywords: finite rank
zbMATH Keywords: fixed points
MaRDI profile type: Publication
full work available at URL: 0195-6698(92)90040-7
OpenAlex ID: W1996837073
cites work: Q4728530
cites work: Q5814844
description: scientific article; zbMATH DE number 64835