# Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields

@article{Gal2014CalculatingAE, title={Calculating all elements of minimal index in the infinite parametric family of simplest quartic fields}, author={Istv{\'a}n Ga{\'a}l and G. G. Petr{\'a}nyi}, journal={Czechoslovak Mathematical Journal}, year={2014}, volume={64}, pages={465-475} }

It is a classical problem in algebraic number theory to decide if a number field is monogeneous, that is if it admits power integral bases. It is especially interesting to consider this question in an infinite parametric familiy of number fields. In this paper we consider the infinite parametric family of simplest quartic fields K generated by a root ξ of the polynomial Pt(x) = x4 − tx3 − 6x2 +tx+1, assuming that t > 0, t ≠ 3 and t2 +16 has no odd square factors. In addition to generators of…

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