Normalizer of an element of a free group The problem says that Let F be the free group on $x_1,x_2, \ldots ,x_n$. Show that the normalizer/centralizer of any element $\neq 1$ is a cyclic group.
The problem seems much harder to me as none of my attempts are anywhere working. Can somebody give me some hints. 

Hint: Let $F$ be a free group. If $a,b \in F$ commute, then $\langle a,b \rangle$ is an abelian subgroup; but it is also free, as a subgroup of a free group. Therefore, $\langle a,b \rangle$ is cyclic.
