2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/72519We prove that if F is a finitely generated free group and f:F -> F is an automorphism with polynomial growth of degree d, then there exists a characteristic subgroup S < F of finite index such that the induced automorphism of the abelianisation of S also grows polynomially of degree d. The proof is geometric in nature and makes use of improved relative train track representatives.59 Pages, 10 figures, excerpt from thesis to be submitted for D.Phil at the University of OxfordGroup Theory20E36, 20E05 (primary); 20F65, 05C25 (secondary)text