An Algorithm That Decides Translation Equivalence in a Free Group of Rank Two
نویسندگان
چکیده
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 φ(u) equals the cyclic length of φ(v) for every automorphism φ 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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