Localization of profinite groups
type: Item
instance of: scholarly article
title: Localization of profinite groups
zbMATH Open document ID: 0544.20026
DOI: 10.1007/BF01198123
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: The authors study the concept of \(\pi\)-local groups and \(\pi\)- localization for profinite groups. It turns out that a profinite group G is \(\pi\)-local if and only if it is a \(\pi\)-group. The main interest then lies on the question whether and how one can construct a profinite group G from its \(\pi\)-localizations \(G_{\pi}\) for \(\pi\) in a given family \(\Pi\) of sets of primes. For a partition \(\Pi\) of the set \({\mathfrak P}\) of all primes this can be done exactly for the direct products of \(\pi\)- groups, \(\pi \in \Pi\). Finally the localizations in the categories of profinite and of abstract groups are compared and sufficient conditions are given under which both coincide.
reviewed by: Norbert Klingen
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20F50
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 3865564
zbMATH Keywords: \(\pi\)-local groups
zbMATH Keywords: \(\pi\)-localization
zbMATH Keywords: profinite groups
author: Wolfgang Herfort
author: Paulo Ribenboim
MaRDI profile type: Publication
cites work: Some aspects of groups with unique roots
cites work: Profinite Frobenius groups
cites work: Tall profinite groups
cites work: Q3292593
full work available at URL: https://doi.org/10.1007/bf01198123
OpenAlex ID: W2088051245
description: scientific article; zbMATH DE number 3865564