\input zb-basic
\input zb-ioport
\iteman{io-port 05817244}
\itemau{Brinkmann, Peter}
\itemti{Detecting automorphic orbits in free groups.}
\itemso{J. Algebra 324, No. 5, 1083-1097 (2010).}
\itemab
The following theorem is the main result of the paper. Theorem. Let $\varphi$ be an automorphism of a finitely generated free group $F$. Then there exists an explicit algorithm that, given two elements $u,v\in F$, decides whether there exists some exponent $N$ such that $u\varphi^N=v$, or whether these elements are conjugate in $F$. If such an exponent $N$ exists, then the algorithms will compute $N$ as well. The main technical tool of the paper is an algorithmic extension of the theory of relative train track maps.
\itemrv{V. A. Roman'kov (Omsk)}
\itemcc{}
\itemut{free group automorphisms; algorithmic improvements of train tracks; decision problems; automorphic orbits}
\itemli{doi:10.1016/j.jalgebra.2010.05.032}
\end