The monomorphism problem in free groups

Ciobanu, Laura ; Houcine, Abderezak

In: Archiv der Mathematik, 2010, vol. 94, no. 5, p. 423-434

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    Let F be a free group of finite rank. We say that the monomorphism problem in F is decidable if there is an algorithm such that, for any two elements u and v in F, it determines whether there exists a monomorphism of F that sends u to v. In this paper we show that the monomorphism problem is decidable and we provide an effective algorithm that solves the problem