2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58875It is well-known that the automorphism towers of infinite centreless groups of cardinality kappa terminate in less than (2^{kappa})^+ steps. But an easy counting argument shows that (2^{kappa})^+ is not the best possible bound. However, in this paper, we will show that it is impossible to find an explicit better bound using ZFC.LogicGroup Theorytext