Hopf Galois structures on Kummer extensions of prime power degree

摘要

Let K be a field of characteristic not p (an odd prime), containing a primitive pn-th root of unity ζ, and let L = K[z] with xpn - a the minimal polynomial of z over K: thus L|K is a Kummer extension, with cyclic Galois group G = σ acting on L via σ(z)=ζz. T. Kohl, 1998, showed that L|K has pn-1 Hopf Galois structures. In this paper we describe these Hopf Galois structures.