A short question. How can i explain that the images of Nielsen automorphisms are transvections and diagonal matrices ?
More specifically if i have an arbitrary n-tuple of elements of Free group with n generators and apply there a sequence of Nielsen automorphisms with purpose to get new reduced m-tuple, how can i see that that the new tuple is a diagonal or a tranvection matrix ?
we know that the map $\psi : Aut(F_n) \to GL_n( \mathbb{Z})$ is an epimorphism.