Let $p$ be a prime number. We say that a number field $F$ satisfies the condition $(H_{p})$ when any tame cyclic extension $N/F$ of degree $p$ has a normal integral basis. We determine all the CM Galois extensions $F/\mbi{Q}$ satisfying $(H_{p})$ for the case $p \geq 5$ , using the action of the complex conjugation on several objects associated to $F$ .
Publié le : 2010-01-15
Classification:
Hilbert-Speiser number field,
normal integral basis,
CM field,
11R33,
11R18
@article{1265380425,
author = {ICHIMURA, Humio},
title = {Hilbert-Speiser number fields and the complex conjugation},
journal = {J. Math. Soc. Japan},
volume = {62},
number = {1},
year = {2010},
pages = { 83-94},
language = {en},
url = {http://dml.mathdoc.fr/item/1265380425}
}
ICHIMURA, Humio. Hilbert-Speiser number fields and the complex conjugation. J. Math. Soc. Japan, Tome 62 (2010) no. 1, pp. 83-94. http://gdmltest.u-ga.fr/item/1265380425/