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The conjugacy problem for free-by-cyclic groups
Martino, Armando; Ventura Capell, Enric
Universitat Politècnica de Catalunya. Departament de Matemàtiques; Universitat Politècnica de Catalunya. MD - Matemàtica Discreta
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.
Àrees temàtiques de la UPC::Matemàtiques i estadística::Àlgebra
Free groups
Group theory
Grups, Teoria de
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