Automorphism groups of nilpotent groups and spaces
type: Item
instance of: scholarly article
title: Automorphism groups of nilpotent groups and spaces
zbMATH Open document ID: 0962.20026
DOI: 10.1016/S0022-4049(99)00043-2
author: P. F. Pickel
author: Joseph Roitberg
published in: Journal of Pure and Applied Algebra
publication date: 2001-01-11T00:00:00Z
review text: In this article the following main results are obtained. Theorem. There exist finitely generated, torsion-free nilpotent groups \(G_1\), \(G_2\) in the same localization genus whose automorphism groups \(\Aut(G_1)\), \(\Aut(G_2)\) are not isomorphic. Corollary. There exist finite, aspherical CW-complexes (indeed, closed smooth manifolds) \(Y_1\), \(Y_2\) in the same localization genus whose automorphism groups \(\Aut(Y_1)\), \(\Aut(Y_2)\) are not isomorphic. More precisely, \(Y_1\), \(Y_2\) are closed, smooth manifolds which are Eilenberg-MacLane spaces \(K(G_1,1)\), \(K(G_2,1)\), where \(G_1\), \(G_2\) are groups of the kind occuring in the theorem.
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20F18
Mathematics Subject Classification ID: 55P10
Mathematics Subject Classification ID: 55P60
zbMATH DE Number: 1501627
zbMATH Keywords: nilpotent groups
zbMATH Keywords: localization genus
zbMATH Keywords: commensurable groups
zbMATH Keywords: automorphism groups
zbMATH Keywords: Eilenberg-McLane spaces
zbMATH Keywords: CW-complexes
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1501627