Currently displaying 1 – 7 of 7

Showing per page

Order by Relevance | Title | Year of publication

Quaternion Extensions of Order 16

Michailov, Ivo — 2005

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 12F12 We describe several types of Galois extensions having as Galois group the quaternion group Q16 of order 16. This work is partially supported by project of Shumen University.

Groups of Order 32 as Galois Groups

Michailov, Ivo — 2007

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 12F12. We find the obstructions to realizability of groups of order 32 as Galois groups over arbitrary field of characteristic not 2. We discuss explicit extensions and automatic realizations as well. This work is partially supported by project of Shumen University

On realizability of p-groups as Galois groups

Michailov, Ivo M.Ziapkov, Nikola P. — 2011

Serdica Mathematical Journal

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.

Galois realizability of groups of orders p 5 and p 6

Ivo Michailov — 2013

Open Mathematics

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.

On Galois cohomology and realizability of 2-groups as Galois groups

Ivo Michailov — 2011

Open Mathematics

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.

On Galois cohomology and realizability of 2-groups as Galois groups II

Ivo Michailov — 2011

Open Mathematics

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....

Page 1

Download Results (CSV)