  In this paper we use the Galois module structure for the classical
parameterizing spaces for elementary p-abelian extensions of a field K to give
necessary and sufficient conditions for the solvability of any embedding
problem which is an extension of Z/p^nZ with elementary p-abelian kernel. This
allows us to count the total number of solutions to a given embedding problem
when the appropriate modules are finite, and leads to some nontrivial automatic
realization and realization multiplicity results for Galois groups.
