2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221374We establish new conditions that prevent the existence of (weak) normal integral bases in tame Galois extensions of number fields. This leads to the following result: under appropriate technical hypotheses, the existence of a normal integral basis in the upper layer of an abelian tower Q \subset K \subset L forces the tower to be split in a very strong sense.17 pages, 4 figures, uses xypic, minor revisions following referee's report. To appear in Annales de L'Institut FourierNumber Theory11R33; 11R18text