An algorithm that decides translation equivalence in a free group of rank two

الأصل · EN

Let F₂ be a free group of rank 2. We prove that there is an algorithm that decides whether or not, for given two elements u, v of F₂, u and v are translation equivalent in F₂, that is, whether or not u and v have the property that the cyclic length of phi(u) equals the cyclic length of phi(v) for every automorphism phi of F₂. This gives an affirmative solution to problem F38a in the online version (http://www.grouptheory.info) of [1] for the case of F₂.