 

Lindsay N. Childs
On Hopf Galois structures and complete groups


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


Abstract
Let L be a Galois extension of K, fields, with Galois
group Γ. We obtain two results. First, if Γ = Hol(Z_{pe}), 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 = (p1)/2 >2 is also prime. If L/K is Galois with group
Γ = Hol(Z_{p}), p a safeprime, then for every group G of cardinality
p(p1) there is an HHopf 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
lc802@math.albany.edu
http://math.albany.edu:8000/~lc802/

