The conjugacy problem for free-by-cyclic groups

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dc.contributor	Universitat Politècnica de Catalunya. Departament de Matemàtiques
dc.contributor	Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
dc.contributor.author	Martino, Armando
dc.contributor.author	Ventura Capell, Enric
dc.date	2004-04
dc.identifier.citation	Martino, A., Ventura, E. "The conjugacy problem for free-by-cyclic groups". 2004.
dc.identifier.uri	http://hdl.handle.net/2117/79985
dc.language.iso	eng
dc.relation	CRM
dc.rights	info:eu-repo/semantics/openAccess
dc.rights	http://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject	Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
dc.subject	Free groups
dc.subject	Group theory
dc.subject	Grups, Teoria de
dc.title	The conjugacy problem for free-by-cyclic groups
dc.type	info:eu-repo/semantics/draft
dc.type	info:eu-repo/semantics/report
dc.description.abstract	We show that the conjugacy problem is solvable in [finitely generated free]-by-cyclic groups, by using a result of O. Maslakova that one can algorithmically find generating sets for the fixed sub- groups of free group automorphisms, and one of P. Brinkmann that one can determine whether two cyclic words in a free group are mapped to each other by some power of a given automorphism. The algorithm effectively computes a conjugating element, if it exists. We also solve the power conjugacy problem and give an algorithm to rec- ognize if two given elements of a finitely generated free group are Reidemeister equivalent with respect to a given automorphism.