On Unramified Galois Extensions Over Maximum Abelian Extensions of Algebraic Number Fields.
Mamoru Asada (1985)
Mathematische Annalen
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Mamoru Asada (1985)
Mathematische Annalen
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Ibadula, Denis (2001)
Analele Ştiinţifice ale Universităţii “Ovidius" Constanţa. Seria: Matematică
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H. Kisilevsky (1983)
Compositio Mathematica
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Michailov, Ivo (2007)
Serdica Mathematical Journal
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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
Alexander Prestel, Christian U. Jensen (1996)
Manuscripta mathematica
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Chipchakov, I. (2004)
Serdica Mathematical Journal
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2000 Mathematics Subject Classification: 11S31 12E15 12F10 12J20. This paper gives a characterization of Henselian discrete valued fields whose finite abelian extensions are uniquely determined by their norm groups and related essentially in the same way as in the classical local class field theory. It determines the structure of the Brauer groups and character groups of Henselian discrete valued strictly primary quasilocal (or PQL-) fields, and thereby, describes the forms...
Martin Epkenhans (1997)
Acta Arithmetica
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Let mℤd ≀ mℤd ≀ mℤd ≀ m
Kurt Girstmair (2007)
Acta Arithmetica
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Leon R. McCulloh (1987)
Journal für die reine und angewandte Mathematik
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Peter Schmid (2014)
Acta Arithmetica
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For a finite group G let 𝒦₂(G) denote the set of normal number fields (within ℂ) with Galois group G which are 2-ramified, that is, unramified outside {2,∞}. We describe the 2-groups G for which 𝒦₂(G) ≠ ∅, and determine the fields in 𝒦₂(G) for certain distinguished 2-groups G appearing (dihedral, semidihedral, modular and semimodular groups). Our approach is based on Fröhlich's theory of central field extensions, and makes use of ring class field constructions (complex multiplication). ...
Satoshi Fujii (2011)
Acta Arithmetica
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Ivo Michailov (2011)
Open Mathematics
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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...
Masakazu Yamagishi (1993)
Journal für die reine und angewandte Mathematik
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Ivo Michailov (2011)
Open Mathematics
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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.