# On realizability of p-groups as Galois groups

Michailov, Ivo M.; Ziapkov, Nikola P.

Serdica Mathematical Journal (2011)

- Volume: 37, Issue: 3, page 173-210
- ISSN: 1310-6600

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topMichailov, Ivo M., and Ziapkov, Nikola P.. "On realizability of p-groups as Galois groups." Serdica Mathematical Journal 37.3 (2011): 173-210. <http://eudml.org/doc/281575>.

@article{Michailov2011,

abstract = {2000 Mathematics Subject Classification: 12F12, 15A66.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.},

author = {Michailov, Ivo M., Ziapkov, Nikola P.},

journal = {Serdica Mathematical Journal},

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; Inverse problem; embedding problem; Galois group; -group; Kummer extension; corestriction; orthogonal representation; Clifford algebra; spinor; modular group; dihedral group; quaternion group; Galois cohomology},

language = {eng},

number = {3},

pages = {173-210},

publisher = {Institute of Mathematics and Informatics Bulgarian Academy of Sciences},

title = {On realizability of p-groups as Galois groups},

url = {http://eudml.org/doc/281575},

volume = {37},

year = {2011},

}

TY - JOUR

AU - Michailov, Ivo M.

AU - Ziapkov, Nikola P.

TI - On realizability of p-groups as Galois groups

JO - Serdica Mathematical Journal

PY - 2011

PB - Institute of Mathematics and Informatics Bulgarian Academy of Sciences

VL - 37

IS - 3

SP - 173

EP - 210

AB - 2000 Mathematics Subject Classification: 12F12, 15A66.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.

LA - eng

KW - Inverse Problem; Embedding Problem; Galois Group; p-Group; Kummer Extension; Corestriction; Orthogonal Representation; Clifford Algebra; Spinor; Modular Group; Dihedral Group; Quaternion Group; Galois Cohomology; Inverse problem; embedding problem; Galois group; -group; Kummer extension; corestriction; orthogonal representation; Clifford algebra; spinor; modular group; dihedral group; quaternion group; Galois cohomology

UR - http://eudml.org/doc/281575

ER -

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