2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/69367We construct an example of an IA-automorphism of the free metabelian group of rank $n\geq 3$ without nontrivial fixed points. That gives a negative answer to the question raised by Shpilrain. By a result of Bachmuth \cite{Ba1}, such an automorphism does not exist if the rank is equal to 2.5 pagesGroup TheoryPrimary 20E05; Secondary 20E36, 22F28text