HNN-extensions of finitely presented soluble groups
type: Item
instance of: scholarly article
title: HNN-extensions of finitely presented soluble groups
zbMATH Open document ID: 0804.20019
author: J. R. J. Groves
published in: Journal of Algebra
publication date: 1995-01-12T00:00:00Z
review text: The author studies some properties of finitely presented soluble groups. He first considers HNN-extensions of such groups, and proves that if \(G\) is any finitely presented nilpotent-by-abelian-by-finite group and \(H\) is any descending HNN-extension of \(G\), then \(H\) is also nilpotent-by- abelian-by-finite. The proof of this result consists largely of commutative algebra. With similar methods he proves that every soluble group of automorphisms of a finitely presented nilpotent-by-abelian-by- finite group is likewise nilpotent-by-abelian-by-finite. This result should be related to the well-known theorem of Mal'cev-Baer that every soluble group of automorphisms of a polycyclic-by-finite group is polycyclic. The author also points out that the above theorems remain true if the hypothesis that the group is finitely presented is replaced by the assumption that it has finite Prüfer rank.
reviewed by: Silvana Franciosi
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F16
Mathematics Subject Classification ID: 20F28
Mathematics Subject Classification ID: 20E22
zbMATH DE Number: 554193
zbMATH Keywords: finitely presented soluble groups
zbMATH Keywords: HNN-extensions
zbMATH Keywords: nilpotent-by-abelian- by-finite groups
zbMATH Keywords: soluble group of automorphisms
zbMATH Keywords: theorem of Mal'cev- Baer
zbMATH Keywords: polycyclic-by-finite groups
zbMATH Keywords: finite Prüfer rank
MaRDI profile type: Publication
full work available at URL: jabr.1993.1238
OpenAlex ID: W2068426200
DOI: 10.1006/JABR.1993.1238
description: scientific article; zbMATH DE number 554193