Let $M=\Q(i\sqrt{d})$ be any imaginary quadratic field with a positivesquare-free $d$. Consider the polynomial\[f(x)=x^3-ax^2-(a+3)x-1,\]with a parameter $a\in\Z$.Let $K=M(\alpha)$, where $\alpha$ is a root of $f$.This is an infinite parametric family of sextic fields dependingon two parameters, $a$ and $d$.Applying relative Thue equationswe determine the relative power integral bases of these sextic fieldsover their quadratic subfields.Using these results we also determine generators of (absolute)power integral bases of the sextic fields.
@article{386,
title = {Power integral bases in a family of sextic fields with quadratic subfields},
journal = {Tatra Mountains Mathematical Publications},
volume = {62},
year = {2015},
doi = {10.2478/tatra.v64i0.386},
language = {EN},
url = {http://dml.mathdoc.fr/item/386}
}
Gaál, István; Remete, László. Power integral bases in a family of sextic fields with quadratic subfields. Tatra Mountains Mathematical Publications, Tome 62 (2015) . doi : 10.2478/tatra.v64i0.386. http://gdmltest.u-ga.fr/item/386/