Reports de recercahttp://hdl.handle.net/2117/799862023-06-08T22:11:41Z2023-06-08T22:11:41ZThe conjugacy problem for free-by-cyclic groupsMartino, ArmandoVentura Capell, Enrichttp://hdl.handle.net/2117/799852020-07-23T21:29:22Z2015-11-26T18:18:08ZThe conjugacy problem for free-by-cyclic groups
Martino, Armando; Ventura Capell, Enric
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.
2015-11-26T18:18:08ZMartino, ArmandoVentura Capell, EnricWe 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.