A proof of the Scott-Wiegold conjecture on free products of cyclic groups

James Howie

Research output: Contribution to journalArticle

13 Citations (Scopus)

Abstract

Problem 5.53 of Mazurov and Khukhro (Unsolved Problems in Group Theory: The Kourovka Notebook, 12th Edition, Russian Academy of Sciences, Novosibirsk, 1992) (contributed by Wiegold, attributed to Scott) asks whether a free product of three (finite) cyclic groups can be normally generated by a single element. We give a proof of the conjectured negative answer, and an application to Dehn surgery on knots: if Dehn surgery on a knot is S3 gives a connected sum, then all but at most 2 of the connected summands are Z-homology spheres, and hence (by a result of Valdez and Sayari) the number of connected summands is at most 3. © 2002 Published by Elsevier Science B.V.

Original languageEnglish
Pages (from-to)167-176
Number of pages10
JournalJournal of Pure and Applied Algebra
Volume173
Issue number2
DOIs
Publication statusPublished - 24 Aug 2002

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