Abstract
ABSTRACT Let be a quadratic extension of fields of characteristic not 2. We give a natural correspondence between cup-products of square classes of and certain Galois embedding problems over . Under this correspondence, the obstruction to the embedding problem associated to is the corestriction from to of the quaternion algebra over given by . We reduce the explicit construction problem for such embedding problems to the construction of an -algebra isomorphism from an algebra expressed as a tensor product of quaternion algebras to a matrix ring. We apply these results to determine the obstructions to, and a method for explicit construction for, all -embedding problems extending or , where the subdirect products are taken over a common factor group .
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