Let be a prime number. We say that a number field satisfies the condition when any tame cyclic extension of degree has a normal integral basis. We determine all the CM Galois extensions satisfying for the case , using the action of the complex conjugation on several objects associated to .
"Hilbert-Speiser number fields and the complex conjugation." J. Math. Soc. Japan 62 (1) 83 - 94, January, 2010. https://doi.org/10.2969/jmsj/06210083