Abstract
In this paper, we study the Hopf-Galois structures on a finite Galois extension whose Galois group G is an almost simple group in which the socle A has prime index p. Each Hopf-Galois structure is associated to a group N of the same order as G. We shall give necessary criteria on these N in terms of their group-theoretic properties, and determine the number of Hopf-Galois structures associated to A×Cp, where Cp is the cyclic group of order p.
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