On realizability of p-groups as Galois groups

2011/12/07 by Ivo M. Michailov, Michailov, Ivo M., Nikola P. Ziapkov +1 · 1 citation
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Geometric and Algebraic Topology #math.AG

paper · pdf · doi:10.48550/arxiv.1112.1522

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

arxiv created 2012/01/05 · arxiv updated 2012/01/06

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.

Cited by

• Inverse Galois Problem and Significant Methods

Related

• Galois p-groups and Galois modules
• Construction of maximal unramified p-extensions with prescribed Galois groups
• p-Groups have unbounded realization multiplicity
• Galois realizability of groups of orders p⁵ and p⁶
• Combinatorial Techniques in the Galois Theory of p-Extensions