On realizability of $p$-groups as Galois groups

Ivo M. Michailov; Nikola P. Ziapkov

On realizability of $p$-groups as Galois groups

Algebraic Geometry 2012-01-06 v2

Authors: Ivo M. Michailov , Nikola P. Ziapkov

Abstract

In this article we survey and examine the realizability of $p$ -groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among $p$ -groups, and related topics.

Keywords

p-groups Galois groups realizability embedding problem cohomological criteria field extensions

Cite

@article{arxiv.1112.1522,
  title  = {On realizability of $p$-groups as Galois groups},
  author = {Ivo M. Michailov and Nikola P. Ziapkov},
  journal= {arXiv preprint arXiv:1112.1522},
  year   = {2012}
}

Comments

In this version is added an example at the end of Section 6. Also, some mistakes are corrected and the references are updated

On realizability of $p$-groups as Galois groups

Abstract

Keywords

Cite

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