On a theorem of Zelmanov
type: Item
instance of: scholarly article
title: On a theorem of Zelmanov
zbMATH Open document ID: 0949.20018
author: John S. Wilson
published in: Journal of Algebra
publication date: 2000-09-05T00:00:00Z
review text: The author gives a new (more direct and short) proof of the result of Zelmanov that a non-cyclic pro-\(p\) group \(G\) satisfying the Golod-Shafarevich inequality contains a nonabelian free pro-\(p\) subgroup. It is proved in addition that a quotient group of \(G\) contains a closed normal subgroup which is a Cartesian product of infinitely many finitely generated infinite pro-\(p\) groups, each of which is an epimorphic image of an open normal subgroup of \(G\).
Mathematics Subject Classification ID: 20E18
Mathematics Subject Classification ID: 20E07
zbMATH DE Number: 1384480
zbMATH Keywords: pro-\(p\) groups
zbMATH Keywords: free pro-\(p\) subgroups
zbMATH Keywords: closed normal subgroups
zbMATH Keywords: open normal subgroups
reviewed by: Pavel Zalesskij
MaRDI profile type: Publication
full work available at URL: jabr.1999.7924
OpenAlex ID: W1986762279
cites work: Q5509036
cites work: Finite presentations of pro-\(p\) groups and discrete groups
cites work: Q4217279
cites work: Identities for Lie algebras of pro-\(p\) groups
cites work: Q4011125
cites work: Q4891348
DOI: 10.1006/JABR.1999.7924
description: scientific article; zbMATH DE number 1384480