Abstract
For a given number field K, does there exist an extension M of odd prime degree l such that the relative discriminant of M/K is a principal ideal, but M/K has no relative integral basis? A general, but incomplete answer is given to this question when K/Q is a normal extension. If, in addition, [ K: Q] is odd, the answer is complete. A detailed study is done when K/Q is a quadratic or normal quartic extension.
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