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Explicit Solutions of Galois Embedding Problems by Means of Generalized Clifford Algebras

In this paper we study Galois embedding problems given by central extensions with cyclic kernel. We find a new expression for the obstruction to the solvability of these embedding problems in terms of Galois symbols. We also give a method to construct the solutions when these problems are solvable. We find a solution from a coordinate of the norm of an adequate element in a generalized Clifford algebra.