New York Journal of Mathematics
Volume 9 (2003) 99-115


Lindsay N. Childs

On Hopf Galois structures and complete groups

Published: August 8, 2003
Keywords: Hopf Galois structure, complete group, holomorph
Subject: 12F, 16W

Let L be a Galois extension of K, fields, with Galois group Γ. We obtain two results. First, if Γ = Hol(Zpe), we determine the number of Hopf Galois structures on L/K where the associated group of the Hopf algebra H is Γ (i.e., L⊗K H ≅ L[Γ]). Now let p be a safeprime, that is, p is a prime such that q = (p-1)/2 >2 is also prime. If L/K is Galois with group Γ = Hol(Zp), p a safeprime, then for every group G of cardinality p(p-1) there is an H-Hopf Galois structure on L/K where the associated group of H is G, and we count the structures.

Author information

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