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