In this paper we develop some new theoretical criteria for the realizability of p-groups as Galois groups over arbitrary fields. We provide necessary and sufficient conditions for the realizability of 14 of the 22 non-abelian 2-groups having a cyclic subgroup of index 4 that are not direct products of groups.
@article{bwmeta1.element.doi-10_2478_s11533-011-0004-4,
author = {Ivo Michailov},
title = {On Galois cohomology and realizability of 2-groups as Galois groups},
journal = {Open Mathematics},
volume = {9},
year = {2011},
pages = {403-419},
zbl = {1256.12004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0004-4}
}
Ivo Michailov. On Galois cohomology and realizability of 2-groups as Galois groups. Open Mathematics, Tome 9 (2011) pp. 403-419. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-011-0004-4/
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