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