Abstract:
|
By using a recent theorem by Koch, Kohl, Truman and Underwood on normality, we determine that some types of Hopf Galois structures do not occur on Galois extensions with Galois group isomorphic to alternating or symmetric groups. Our theory of induced Hopf Galois structures allows us to obtain the whole picture of types of Hopf Galois structures on A4-extensions, S4-extensions, and S5-extensions. Combining it with a result of Carnahan and Childs, we obtain a complete count of the Hopf Galois structures on S5-extensions. |