Geodesic
On realizability of p-groups as Galois groups
Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 173-210.

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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: Inverse Problem, Embedding Problem, Galois Group, p-Group, Kummer Extension, Corestriction, Orthogonal Representation, Clifford Algebra, Spinor, Modular Group, Dihedral Group, Quaternion Group, Galois Cohomology 
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     title = {On realizability of p-groups as {Galois} groups},
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Michailov, Ivo M.; Ziapkov, Nikola P. On realizability of p-groups as Galois groups. Serdica Mathematical Journal, Tome 37 (2011) no. 3, pp. 173-210. http://geodesic.mathdoc.fr/item/SMJ2_2011_37_3_a0/