Realizability and automatic realizability of Galois groups of order 32

Helen Grundman; Tara Smith

Displaying similar documents to “Realizability and automatic realizability of Galois groups of order 32”

On the inverse problem of Galois theory.

Núria Vila (1992)

Publicacions Matemàtiques

Similarity:

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.

The Galois relation x₁ = x₂ + x₃ for finite simple groups

Kurt Girstmair (2007)

Acta Arithmetica

Similarity:

Remarks on the intrinsic inverse problem

Daniel Bertrand (2002)

Banach Center Publications

Similarity:

The intrinsic differential Galois group is a twisted form of the standard differential Galois group, defined over the base differential field. We exhibit several constraints for the inverse problem of differential Galois theory to have a solution in this intrinsic setting, and show by explicit computations that they are sufficient in a (very) special situation.

Small Galois groups that encode valuations

Ido Efrat, Ján Mináč (2012)

Acta Arithmetica

Similarity:

Galois realizability of groups of order 64

Helen Grundman, Tara Smith (2010)

Open Mathematics

Similarity:

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.

On the Beckmann-Black problem

Nour Ghazi (2011)

Acta Arithmetica

Similarity:

Groups of Order 32 as Galois Groups

Michailov, Ivo (2007)

Serdica Mathematical Journal

Similarity:

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

On realizability of p-groups as Galois groups

Michailov, Ivo M., Ziapkov, Nikola P. (2011)

Serdica Mathematical Journal

Similarity:

2000 Mathematics Subject Classification: 12F12, 15A66. In this article we survey and examine the realizability of p-groups as Galois groups over arbitrary fields. In particular we consider various cohomological criteria that lead to necessary and sufficient conditions for the realizability of such a group as a Galois group, the embedding problem (i.e., realizability over a given subextension), descriptions of such extensions, automatic realizations among p-groups, and related...

On the computation of resolvents and Galois groups.

Kurt Girstmair (1983)

Manuscripta mathematica

Similarity:

Invariants and differential Galois groups in degree four

Julia Hartmann (2002)

Banach Center Publications

Similarity:

This note extends the algorithm of [hess] for computing unimodular Galois groups of irreducible differential equations of order four. The main tool is invariant theory.