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

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

2006-10-27

arxiv.org/abs/math/0610833v1

J. Group Theory, vol.10 (2007), pp.561-569

Mathematics

Group Theory

11 pages

Scientific paper

Let F_2 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 F_2, u and v are translation equivalent in F_2, 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 F_2. This gives an affirmative solution to problem F38a in the online version (http://www.grouptheory.info) of [1] for the case of F_2.

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