Hopf Galois theory of separable field extensions

Abstract

Hopf Galois theory is a generalization of Galois theory. Galois theory gives a bijective correspondence between intermediate fields of a Galois field extension (normal and separable) and subgroups of the Galois group. Hopf Galois theory substitutes the Galois group by a Hopf algebra. In the case of separable extensions it has a characterization of the Hopf Galois character in terms of groups. Thus, we use Magma in order to obtain all Hopf Galois structures of extensions of degree 8.