Small maximal pro-p Galois groups.
Ido Efrat (1998)
Manuscripta mathematica
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Ido Efrat (1998)
Manuscripta mathematica
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Helen Grundman, Tara Smith (2010)
Open Mathematics
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This article examines the realizability of groups of order 64 as Galois groups over arbitrary fields. Specifically, we provide necessary and sufficient conditions for the realizability of 134 of the 200 noncyclic groups of order 64 that are not direct products of smaller groups.
Jochen Koenigsmann (1998)
Manuscripta mathematica
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Roger Ware, Ján Minác (1991)
Manuscripta mathematica
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Kurt Girstmair (1983)
Manuscripta mathematica
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Núria Vila (1992)
Publicacions Matemàtiques
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The problem of the construction of number fields with Galois group over Q a given finite groups has made considerable progress in the recent years. The aim of this paper is to survey the current state of this problem, giving the most significant methods developed in connection with it.
Helen Grundman, Tara Smith (2010)
Open Mathematics
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This article provides necessary and sufficient conditions for each group of order 32 to be realizable as a Galois group over an arbitrary field. These conditions, given in terms of the number of square classes of the field and the triviality of specific elements in related Brauer groups, are used to derive a variety of automatic realizability results.
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
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.
B. Heinrich Matzat (1985)
Manuscripta mathematica
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Gudrun Brattström (1989)
Mathematica Scandinavica
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Claude Mitschi, Michael F. Singer (2002)
Annales de la Faculté des sciences de Toulouse : Mathématiques
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Helmut Völklein (1992)
Mathematische Annalen
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T.M. Viswanathan, A.J. Engler (1986)
Manuscripta mathematica
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Ido Efrat, Ján Mináč (2012)
Acta Arithmetica
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M. Madan, M. Rzedowski-Calderón (1996)
Manuscripta mathematica
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