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

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

2011-09-19

arxiv.org/abs/1109.4071v2

Mathematics

Number Theory

30 pages; updated references in second version

Scientific paper

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.

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