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
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- [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 Zbl0849.12006
- [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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