Inverse Problem Embedding Problem Galois Group p-Group Kummer Extension Corestriction Orthogonal Representation Clifford Algebra Spinor Modular Group Dihedral Group Quaternion Group Galois Cohomology
Issue Date:
2011
Publisher:
Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Citation:
Serdica Mathematical Journal, Vol. 37, No 3, (2011), 173p-210p
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.
