Free-by-cyclic groups have solvable conjugacy problem

Details Free-by-cyclic groups have solvable conjugacy problem Free-by-cyclic groups have solvable conjugacy problem

2004-05-10

arxiv.org/abs/math/0405178v2

Mathematics

Group Theory

8 pages, submitted

Scientific paper

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 subgroups 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 recognize if two given elements of a finitely generated free group are Reidemeister equivalent with respect to a given automorphism.

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