Twisted conjugacy in free groups and Makanin's question

Abstract

We discuss the following question of G. Makanin from ``Kourovka notebook'': does there exist an algorithm to determine is for an arbitrary pair of words $U$ and $V$ of a free group $F_n$ and an arbitrary automorphism $\varphi \in Aut(F_n)$ the equation $\varphi (X)U=VX$ solvable in $F_n$? We give the affirmative answer in the case when an automorphism is virtually inner, i.e. some its non-zero power is an inner automorphism of $F_n$.

19 pages

References in corpus (1)

• Free-by-cyclic groups have solvable conjugacy problem

Cited by in corpus (2)

• Free-by-cyclic groups have solvable conjugacy problem
• On the conjugacy problem for cyclic extensions of free groups