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

• Autorzy: Ivo Michailov
• Języki publikacji: EN

Abstrakty

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.

Słowa kluczowe

EN

Embedding problem; Galois extension; Quaternion algebra; Obstruction; Free resolution; Free abelian group

Kategorie tematyczne

• 12F12: Inverse Galois theory

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2011
• Tom: 9
• Numer: 6
• Strony: 1333-1343

Daty

wydano

2011-12-01

online

2011-09-23

Twórcy

autor

Ivo Michailov

• Episkop Constantin Preslavski University

Bibliografia

• [1] Ishanov V.V., Lur’e B.B., Faddeev D.K., The Embedding Problem in Galois Theory, Transl. Math. Monogr., 165, American Mathematical Society, Providence, 1997
• [2] Ledet A., On 2-groups as Galois groups, Canad. J. Math., 1995, 47(6), 1253–1273 http://dx.doi.org/10.4153/CJM-1995-064-3
• [3] Michailov I.M., Induced orthogonal representations of Galois groups, J. Algebra, 2009, 322(10), 3713–3732 http://dx.doi.org/10.1016/j.jalgebra.2009.07.035
• [4] Michailov I.M., On Galois cohomology and realizability of 2-groups as Galois groups, Cent. Eur. J. Math., 2011, 9(2), 403–419 http://dx.doi.org/10.2478/s11533-011-0004-4
• [5] Michailov I.M., Ziapkov N.P., Embedding obstructions for the generalized quaternion group, J. Algebra, 2000, 226(1), 375–389 http://dx.doi.org/10.1006/jabr.1999.8190
• [6] Ninomiya Y., Finite p-groups with cyclic subgroups of index p 2, Math. J. Okayama Univ., 1994, 36, 1–21
• [7] Speiser A., Zahlentheoretische Sätze aus der Gruppentheorie, Math. Z., 1919, 5(1–2), 1–6 http://dx.doi.org/10.1007/BF01203150

Identyfikatory

DOI

10.2478/s11533-011-0086-z