On the trace map between absolutely abelian number fields of equal conductor
On totally real Hilbert-Speiser fields of type Cₚ
Non-existence and splitting theorems for normal integral bases
We 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 forces the tower to be split in a very strong sense.
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