On finite Abelian groups realizable as Mislin genera
type: Item
instance of: scholarly article
title: On finite Abelian groups realizable as Mislin genera
zbMATH Open document ID: 0897.20025
DOI: 10.5565/PUBLMAT_41297_14
published in: Publicacions Matemàtiques
publication date: 1998-10-20T00:00:00Z
full work available at URL: https://eudml.org/doc/41308
review text: The Mislin genus of a finitely generated nilpotent group \(N\) is the set of isomorphism classes of finitely generated nilpotent groups \(M\) having, at each prime \(p\), a localization isomorphic with that of \(N\), i.e. \(M_p\cong N_p\) for all \(p\). The authors study the realizability of finite Abelian groups as Mislin genera of finitely generated nilpotent groups with finite commutator subgroup. In particular, they give criteria to decide whether a finite Abelian group is realizable as the Mislin genus of a direct product of nilpotent groups of a certain specified type. In the case of a positive answer, the authors give an effective way of realizing that Abelian group as a genus. Further, some non-realizability results are obtained.
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 1146199
zbMATH Keywords: finitely generated nilpotent groups
zbMATH Keywords: localizations
zbMATH Keywords: finite Abelian groups
zbMATH Keywords: Mislin genera
zbMATH Keywords: direct products of nilpotent groups
author: Peter Hilton
author: Dirk Scevenels
reviewed by: Alexander Ivanovich Budkin
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1146199