On Hopf Galois structures and complete groups
نویسنده
چکیده
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.
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