New York Journal of Mathematics
Volume 17 (2011) 51-74


Lindsay N. Childs

Hopf Galois structures on Kummer extensions of prime power degree

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Published: February 24, 2011
Keywords: Hopf Galois extension, Kummer extension, p-adic logarithm
Subject: 12F10

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.

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Department of Mathematics and Statistics, University at Albany, Albany, NY 12222