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Galois realizability of groups of orders p 5 and p 6

100%
Michailov I.
Open Mathematics
|
2013
|
tom 11
|
nr 5
910-923
EN
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.
2
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Noether's problem for some groups of order 16n

100%
Michailov I.
Acta Arithmetica
|
2010
|
tom 143
|
nr 3
277-290
3
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On Galois cohomology and realizability of 2-groups as Galois groups

100%
Michailov I.
Open Mathematics
|
2011
|
tom 9
|
nr 2
403-419
EN
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.
4
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On Galois cohomology and realizability of 2-groups as Galois groups II

100%
Michailov I.
Open Mathematics
|
2011
|
tom 9
|
nr 6
1333-1343
EN
In [Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419] we calculated the obstructions to the realizability as Galois groups of 14 non-abelian groups of order 2n, n ≥ 4, having a cyclic subgroup of order 2n−2, over fields containing a primitive 2n−3th root of unity. In the present paper we obtain necessary and sufficient conditions for the realizability of the remaining 8 groups that are not direct products of smaller groups.
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