Parameterizing solutions to any Galois embedding problem over Z/p^nZ with elementary p-abelian kernel
Number Theory
2014-03-28 v3
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.
Cite
@article{arxiv.1109.4071,
title = {Parameterizing solutions to any Galois embedding problem over Z/p^nZ with elementary p-abelian kernel},
author = {Andrew Schultz},
journal= {arXiv preprint arXiv:1109.4071},
year = {2014}
}
Comments
37 pages; updated references in second version; exposition improved in the third version