Computing centralizers in [f.g. free]-by-cyclic groups

Abstract

We prove that centralizers of elements in [f.g. free]-by-cyclic groups are computable. As a corollary we get that, given two conjugate elements in a [f.g. free]-by-cyclic group, the set of conjugators can be computed and that the conjugacy problem with context-free constraints is decidable. In the end, we pose several problems arising naturally from this work.