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

Open Mathematics (2011)

- Volume: 9, Issue: 6, page 1333-1343
- ISSN: 2391-5455

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topIvo Michailov. "On Galois cohomology and realizability of 2-groups as Galois groups II." Open Mathematics 9.6 (2011): 1333-1343. <http://eudml.org/doc/269627>.

@article{IvoMichailov2011,

abstract = {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.},

author = {Ivo Michailov},

journal = {Open Mathematics},

keywords = {Embedding problem; Galois extension; Quaternion algebra; Obstruction; Free resolution; Free abelian group; embedding problem; quaternion algebra; obstruction; free resolution; free abelian group},

language = {eng},

number = {6},

pages = {1333-1343},

title = {On Galois cohomology and realizability of 2-groups as Galois groups II},

url = {http://eudml.org/doc/269627},

volume = {9},

year = {2011},

}

TY - JOUR

AU - Ivo Michailov

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

JO - Open Mathematics

PY - 2011

VL - 9

IS - 6

SP - 1333

EP - 1343

AB - 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.

LA - eng

KW - Embedding problem; Galois extension; Quaternion algebra; Obstruction; Free resolution; Free abelian group; embedding problem; quaternion algebra; obstruction; free resolution; free abelian group

UR - http://eudml.org/doc/269627

ER -

## References

top- [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
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- [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 Zbl1216.12005
- [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 Zbl1256.12004
- [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 Zbl0973.12003
- [6] Ninomiya Y., Finite p-groups with cyclic subgroups of index p 2, Math. J. Okayama Univ., 1994, 36, 1–21 Zbl0838.20017
- [7] Speiser A., Zahlentheoretische Sätze aus der Gruppentheorie, Math. Z., 1919, 5(1–2), 1–6 http://dx.doi.org/10.1007/BF01203150 Zbl47.0092.01

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