Amalgam decompositions for one-relator groups
type: Item
instance of: scholarly article
title: Amalgam decompositions for one-relator groups
zbMATH Open document ID: 0932.20023
DOI: 10.1016/S0022-4049(99)00052-3
author: Benjamin Fine
author: Ada Peluso
published in: Journal of Pure and Applied Algebra
publication date: 2000-03-07T00:00:00Z
review text: Let \(G\) be a finitely presented group. A decomposition (if it exists) of \(G\) as a proper free product with amalgamation \((A*B:C)\) with the factors \(A\) and \(B\) and the amalgamated subgroup \(C\) all finitely generated is called a Baumslag-Shalen decomposition. It is known that \(G\) has a Baumslag-Shalen decomposition if the deficiency of \(G\) is greater than one. Especially, a one-relator group \(G\) with at least three generators admits a Baumslag-Shalen decomposition. In this latter special situation the authors prove some results about the exact nature of the factors \(A\) and \(B\) of the decomposition.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 1340426
zbMATH Keywords: finitely presented groups
zbMATH Keywords: free products with amalgamation
zbMATH Keywords: Baumslag-Shalen decompositions
zbMATH Keywords: deficiency
zbMATH Keywords: one-relator groups
reviewed by: Gerhard Rosenberger
MaRDI profile type: Publication
Wikidata QID: Q127972623
full work available at URL: s0022-4049(99)00052-3
OpenAlex ID: W2021976774
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description: scientific article; zbMATH DE number 1340426