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If L/K is a Galois extension of fields with Galois group Gamma, then the K-Hopf algebra K Gamma acts on L and makes L/K into a Hopf Galois extension. But there may be many other Hopf Galois structures on L/K arising from K-Hopf algebras H other than KGamma. Each such H satisfies L \otimes_{K} H ~= LG for some group G, called the associated group of H.We discuss two new results. One is to count Hopf Galois structures on L/K for a suitable Gamma where the associated group G is an elementary abelian p-group of order p^{m}, complementing Steve Featherstonhaugh's doctoral thesis; the other is to look at Hopf Galois structures when Gamma = G is a semidirect product of two finite cyclic groups, based on Jesse Corradino's honors thesis.
Refreshments at 4:00 pm in ES 152