A virtually free pro-\(p\) need not be the fundamental group of a profinite graph of finite groups.
type: Item
instance of: scholarly article
title: A virtually free pro-\(p\) need not be the fundamental group of a profinite graph of finite groups.
zbMATH Open document ID: 1193.20032
author: Pavel Zalesskij
author: Wolfgang Herfort
published in: Archiv der Mathematik
publication date: 2010-02-25T00:00:00Z
review text: According to a celebrated result of \textit{J.-P.~Serre}, a torsion-free pro-\(p\) group that contains an open free pro-\(p\) group is itself free pro-\(p\) [Topology 3, 413-420 (1965; Zbl 0136.27402)]. The authors of the paper under review have extended this result to finitely generated pro-\(p\) groups [preprint (2007)]. The latter result is a pro-\(p\) analogue of a description of virtually free discrete groups, which does not depend on the cardinality of a set of generators. The goal of this note is to exhibit a countably generated pro-\(p\) group for which the corresponding result fails.
reviewed by: Andrea Caranti
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20E06
zbMATH DE Number: 5675001
zbMATH Keywords: pro-\(p\) groups
zbMATH Keywords: virtual freeness
zbMATH Keywords: pro-\(p\) trees
MaRDI profile type: Publication
full work available at URL: s00013-009-0063-y
OpenAlex ID: W2065790400
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DOI: 10.1007/S00013-009-0063-Y
description: scientific article; zbMATH DE number 5675001