Let p be an odd prime and k an arbitrary field of characteristic not p. We determine the obstructions for the realizability as Galois groups over k of all groups of orders p 5 and p 6 that have an abelian quotient obtained by factoring out central subgroups of order p or p 2. These obstructions are decomposed as products of p-cyclic algebras, provided that k contains certain roots of unity.
@article{bwmeta1.element.doi-10_2478_s11533-013-0217-9,
author = {Ivo Michailov},
title = {Galois realizability of groups of orders p 5 and p 6},
journal = {Open Mathematics},
volume = {11},
year = {2013},
pages = {910-923},
zbl = {1279.12006},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0217-9}
}
Ivo Michailov. Galois realizability of groups of orders p 5 and p 6. Open Mathematics, Tome 11 (2013) pp. 910-923. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0217-9/
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