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16.110 (2006)

Open

(I. Kapovich, P. Schupp). Is there an algorithm which, when given two elements $u, v$ of a free group $F_n$, decides whether or not the cyclic length of $\phi(u)$ equals the cyclic length of $\phi(v)$ for every automorphism $\phi$ of $F_n$?

Contributor: V. E. Shpilrain

Progress

Comment of 2009: The answer was shown to be positive for $n = 2$ in (D. Lee, J. Group Theory, 10 (2007), 561–569).

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