The Bianchi groups are separable on geometrically finite subgroups.
type: Item
instance of: scholarly article
title: The Bianchi groups are separable on geometrically finite subgroups.
zbMATH Open document ID: 1067.20067
DOI: 10.2307/2661363
published in: Annals of Mathematics. Second Series
publication date: 2004-08-05T00:00:00Z
full work available at URL: issues.html
review text: Let \(G\) be a group and \(H\) a finitely generated subgroup; \(G\) is called `\(H\)-subgroup separable' if for every \(g\in G\setminus H\) there is a subgroup \(K\subset G\) of finite index such that \(H\subset K\) and \(g\notin K\). A Kleinian group \(G\) is called `geometrically finite' if \(G\) admits a finite-sided Dirichlet polyhedron for its action on \(\mathbb{H}^3\). The main result is that the group \(\text{PSL}(2,{\mathcal O}_d)\) is \(H\)-subgroup separable for geometrically finite subgroups \(H\). Here \(d\) is any square free positive integer and \({\mathcal O}_d\) is the ring of integers in \(\mathbb{Q}(\sqrt{-d})\).
Mathematics Subject Classification ID: 20H10
Mathematics Subject Classification ID: 11F06
Mathematics Subject Classification ID: 20E26
Mathematics Subject Classification ID: 30F40
zbMATH DE Number: 2081321
zbMATH Keywords: Bianchi groups
zbMATH Keywords: subgroup separable groups
zbMATH Keywords: Kleinian groups
zbMATH Keywords: subgroups of finite index
author: Ian Agol
author: D. D. Long
author: Alan W. Reid
reviewed by: L. N. Vaserstein
MaRDI profile type: Publication
OpenAlex ID: W2158582567
description: scientific article; zbMATH DE number 2081321