A non-Hopfian automatic group
type: Item
instance of: scholarly article
title: A non-Hopfian automatic group
zbMATH Open document ID: 0848.20028
author: Daniel T. Wise
published in: Journal of Algebra
publication date: 1996-10-28T00:00:00Z
review text: The author considers a finitely generated group \(G=\langle a, b, s, t\rangle\) with the following defining relators \([a,b]=1\), \(a^s=(ab)^2\), \(b^t=(ab)^2\). He proves the following results about the group \(G\). Theorem 1. \(G\) is not Hopfian. Theorem 2. \(G\) is an automatic group. Theorem 3. \(G\) is \(\pi_1\) of a compact nonpositively curved 2-complex.
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E36
Mathematics Subject Classification ID: 57M05
zbMATH DE Number: 870168
zbMATH Keywords: non-Hopfian groups
zbMATH Keywords: finitely generated groups
zbMATH Keywords: relators
zbMATH Keywords: automatic groups
reviewed by: L. A. Kurdachenko
MaRDI profile type: Publication
full work available at URL: jabr.1996.0096
OpenAlex ID: W2090649107
DOI: 10.1006/JABR.1996.0096
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description: scientific article; zbMATH DE number 870168