Explicit solutions of Galois embedding problems by means of generalized Clifford algebras

In this paper we study Galois embedding problems given by central extension s with cyclic kernel. We find a new expression for the obstruction to the s olvability 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. (C) 2000 Academic Press.