Power Bases in Dihedral Quartic Fields

Power Integral Bases in the Family of Simplest Quartic Fields

Difference Bases in Dihedral Groups

A subset B of a group G is called a difference basis of G if each element g ∈ G can be written as the difference g = ab−1 of some elements a, b ∈ B. The smallest cardinality |B| of a difference basis B ⊂ G is called the difference size of G and is denoted by ∆[G]. The fraction ð[G] := ∆[G]/ √ |G| is called the difference characteristic of G. We prove that for every n ∈ N the dihedral group D2n ...

On the Resolution of Index Form Equations in Dihedral Quartic Number Fields

Ga al is grateful to the Alexander von Humboldt Stiftung for supporting his work and also to the Mathematisches Institut der Heinrich{Heine{Universit at D usseldorf for its hospitality during his stay there as a Humboldt fellow. Peth} o was supported by Hungarian National Foundation for Scienti c Research Grant 1641/90. Pohst was supported by the Deutsche Forschungsgemeinschaft. We describe a...

On Power Bases in Number Fields

We survey the problem of existence and computation of power bases in number fields.

Power integral bases in sextic fields with a cubic subfield

In the present paper we give an algorithm to compute generators of power integral bases having ”small” coordinates in an integral basis in sextic fields containing a cubic subfield. As an application of the method, we give a sufficient condition for infinite parametric families of number fields of this type to have power integral basis. To illustrate the statement we construct parametric famili...