Pro-forests and nearly free profinite groups.
type: Item
instance of: scholarly article
title: Pro-forests and nearly free profinite groups.
zbMATH Open document ID: 1230.20027
author: Bruno Deschamps
author: Ivan Suarez Atias
published in: Mathematische Annalen
publication date: 2011-06-03T00:00:00Z
review text: A group \(G\) is free if and only if there is a tree \(X\) on which \(G\) acts so that: \(G\) acts freely on \(X\), that is, no element of \(G\) except the identity has fixed points on \(X\); and \(G\) acts without inversions, that is, given any orientation of the tree, no element of \(G\) reverses an edge [see \textit{J.-P. Serre}, ``Arbres, amalgames, \(\mathrm{SL}_2\)'', Astérisque 46 (1977; Zbl 0369.20013)]. The goal of the paper under review is to extend this result to profinite groups. The main theorem states that a profinite group is nearly free, that is, it contains a dense abstract free group, if and only if it acts profreely on a protree. We refer to the paper for the details of the definitions of these terms.
reviewed by: Andrea Caranti
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20E08
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 05C05
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 5903697
zbMATH Keywords: profinite groups
zbMATH Keywords: groups acting on trees
zbMATH Keywords: protrees
zbMATH Keywords: profinite actions
zbMATH Keywords: dense abstract free subgroups
MaRDI profile type: Publication
full work available at URL: s00208-010-0566-7
OpenAlex ID: W1966499119
cites work: Field Arithmetic
cites work: Q4490702
cites work: Q4217279
DOI: 10.1007/S00208-010-0566-7
description: scientific article; zbMATH DE number 5903697