HOPF-GALOIS STRUCTURES OF ISOMORPHIC-TYPE ON A NON-ABELIAN CHARACTERISTICALLY SIMPLE EXTENSION

摘要

Let L/K be a finite Galois extension whose Galois group G is non-abelian and characteristically simple. By drawing tools from graph theory and group theory, we shall give a closed formula for the total number of Hopf-Galois structures on L/K with associated group isomorphic to G.