Galois p-groups and Galois modules
Number Theory
2016-10-21 v2
Abstract
The smallest non-abelian p-groups play a fundamental role in the theory of Galois p-extensions. We illustrate this by highlighting their role in the definition of the norm residue map in Galois cohomology. We then determine how often these groups --- as well as other closely related, larger p-groups --- occur as Galois groups over given base fields. We show further how the appearance of some Galois groups forces the appearance of other Galois groups in an interesting way.
Cite
@article{arxiv.1411.6495,
title = {Galois p-groups and Galois modules},
author = {Sunil Chebolu and Jan Minac and Andrew Schultz},
journal= {arXiv preprint arXiv:1411.6495},
year = {2016}
}
Comments
28 pages. To appear in Rocky Mountain Journal of Mathematics. Version 2 includes some minor corrections