Parameterizing solutions to any Galois embedding problem over Z/p^nZ with elementary p-abelian kernel

Abstract

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.

arXiv comment37 pages; updated references in second version; exposition improved in the third version

Cited by in corpus (2)

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• On the indecomposability of a remarkable new family of modules appearing in Galois theory