Free-by-cyclic groups have solvable conjugacy problem

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 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.

8 pages, submitted

References in corpus (1)

• Twisted conjugacy in free groups and Makanin's question

Cited by in corpus (10)

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• Orbit decidability and the conjugacy problem for some extensions of groups
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• Twisted conjugacy in braid groups
• Word and Conjugacy Problems in Groups $G_{k+1}^k$
• Bitwisted Burnside-Frobenius theorem and Dehn conjugacy problem
• The quadratic isoperimetric inequality for mapping tori of free group automorphisms