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Displaying similar documents to “Pro-2-Demuskin groups of rank ...0 as Galois groups of maximal 2-extensions of fields.”

Groups of Order 32 as Galois Groups

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

Galois realizability of groups of order 64

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.

Finite-dimensional differential algebraic groups and the Picard-Vessiot theory

Anand Pillay (2002)

Banach Center Publications

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We make some observations relating the theory of finite-dimensional differential algebraic groups (the ∂₀-groups of [2]) to the Galois theory of linear differential equations. Given a differential field (K,∂), we exhibit a surjective functor from (absolutely) split (in the sense of Buium) ∂₀-groups G over K to Picard-Vessiot extensions L of K, such that G is K-split iff L = K. In fact we give a generalization to "K-good" ∂₀-groups. We also point out that the "Katz group" (a certain linear...

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

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.