\(P\)-nilpotent completion is not idempotent
type: Item
instance of: scholarly article
title: \(P\)-nilpotent completion is not idempotent
zbMATH Open document ID: 0897.20027
DOI: 10.5565/PUBLMAT_41297_12
published in: Publicacions Matemàtiques
publication date: 1998-10-20T00:00:00Z
full work available at URL: https://eudml.org/doc/41311
review text: Let \(P\) be an arbitrary set of primes. It is proved that the \(P\)-nilpotent completion of an infinitely generated free group \(F\) does not induce an isomorphism on the first homology group with \(\mathbb{Z}_p\) coefficients. As a consequence, the \(P\)-nilpotent completion is not idempotent and any infinite wedge of circles is \(R\)-bad, where \(R\) is any subring of the rationals.
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20J05
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1146197
zbMATH Keywords: \(P\)-nilpotent completions
zbMATH Keywords: infinitely generated free groups
zbMATH Keywords: first homology groups
zbMATH Keywords: wedges of circles
author: Geok-Choo Tan
MaRDI profile type: Publication
OpenAlex ID: W2124230666
description: scientific article; zbMATH DE number 1146197