Some Hopf Galois structures arising from elementary abelian $p$-groups

Abstract

Let p be an odd prime, G =Z m p , the elementary abelian p-group of rank m, and let Γ be the group of principal units of the ring Fp [x]/(x m+1 ). If L/K is a Galois extension with Galois group Γ, then we show that for p > 5, the number of Hopf Galois structures on L/K afforded by K-Hopf algebras with associated group G is greater than p s , where s = (m-1) 2 3- m.