On proper powers in free products and Dehn surgery
type: Item
instance of: scholarly article
title: On proper powers in free products and Dehn surgery
zbMATH Open document ID: 0649.20026
DOI: 10.1016/0022-4049(88)90061-8
author: Steven Boyer
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: The author proves the following theorem: (which was also proved independently by Baumslag, Morgan and Shalen). Let p, q and r be integers greater than or equal to 2, then for any word \(w\in {\mathbb{Z}}/p*{\mathbb{Z}}/q\) \(({\mathbb{Z}}/p*{\mathbb{Z}}/q)/<\omega\) \(r>\not\cong \{e\}\). (Here, the symbol `*' denotes the free product operation between groups and `\(<\omega\) \(r>'\) denotes the normal closure of \(\omega\) r in \({\mathbb{Z}}/p*{\mathbb{Z}}/q.)\) There are some interesting topological applications to knot theory and Dehn surgery.
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 57M35
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 57M25
zbMATH DE Number: 4059686
zbMATH Keywords: words
zbMATH Keywords: free products
zbMATH Keywords: normal closures
zbMATH Keywords: knots
zbMATH Keywords: Dehn surgery
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90061-8
OpenAlex ID: W2000327458
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description: scientific article; zbMATH DE number 4059686