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This paper is devoted to some variants of the Hilbert specialization property. For example, the RG-hilbertian property (for a field K), which arose in connection with the Inverse Galois Problem, requires that the specialization property holds solely for extensions of K(T) that are Galois and regular over K. We show that fields inductively obtained from a real hilbertian field by adjoining real pth roots (p odd prime) are RG-hilbertian; some of these fields are not hilbertian. There are other variants...

An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$

Florent Jouve, Emmanuel Kowalski, David Zywina (2008)

Journal de Théorie des Nombres de Bordeaux

Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group $G$ over $Q$ typically have splitting field with Galois group isomorphic to the Weyl group of $G$ , we construct an explicit monic integral polynomial of degree $240$ whose splitting field has Galois group the Weyl group of the exceptional group of type $E_{8}$ .

Asymptotics of number fields and the Cohen–Lenstra heuristics

Jürgen Klüners (2006)

Journal de Théorie des Nombres de Bordeaux

We study the asymptotics conjecture of Malle for dihedral groups $D_{ℓ}$ of order $2 ℓ$ , where $ℓ$ is an odd prime. We prove the expected lower bound for those groups. For the upper bounds we show that there is a connection to class groups of quadratic number fields. The asymptotic behavior of those class groups is predicted by the Cohen–Lenstra heuristics. Under the assumption of this heuristic we are able to prove the expected upper bounds.

Automatic realizations of Galois groups with cyclic quotient of order $p^{n}$

Ján Mináč, Andrew Schultz, John Swallow (2008)

Journal de Théorie des Nombres de Bordeaux

We establish automatic realizations of Galois groups among groups $M ⋊ G$ , where $G$ is a cyclic group of order $p^{n}$ for a prime $p$ and $M$ is a quotient of the group ring $𝔽_{p} [G]$ .

Braid group action, embedding problems and the groups PGLn(q), Pun(q2).

Helmut Völklein (1994)

Forum mathematicum

Central extensions of the alternating group as Galois groups

Teresa Crespo (1994)

Acta Arithmetica

Construction of a regular extension of $ℚ (T)$ with Galois group $M_{24}$ . (Construction d'une extension régulière de $ℚ (T)$ de groupe de Galois $M_{24}$ .)

Granboulan, Louis (1996)

Experimental Mathematics

Delta-composantes des espaces de modules de revêtements

Orlando Cau (2012)

Journal de Théorie des Nombres de Bordeaux

Nous nous intéressons aux composantes irréductibles des espaces de modules de G-revêtements et à leurs corps de définition. Nos résultats permettent de construire, quel que soit le groupe fini, de telles composantes définies sur $ℚ$ . Notre méthode laisse de plus une grande latitude quant au type de ramification des revêtements. Ces composantes sont obtenues par déformation de certains revêtements du bord des espaces de modules. Enfin, ces composantes sont aussi compatibles dans une tour d’espaces...

An effective construction of homogeneous linear differential equations of order 2 with Galois group $2 A_{4}, 2 S_{4}$ or $2 A_{5}$ is presented.

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A GAP package for braid orbit computation and applications.

Absolute Galois Groups of p-Adically Maximal PpC Fields.

Algebraic covers : field of moduli versus field of definition

Algebraic realization of $p$ -adically projective groups

Almost hilbertian fields

An explicit integral polynomial whose splitting field has Galois group $W (E_{8})$

Asymptotics of number fields and the Cohen–Lenstra heuristics

Automatic realizations of Galois groups with cyclic quotient of order $p^{n}$

Braid group action, embedding problems and the groups PGLn(q), Pun(q2).

Central extensions of the alternating group as Galois groups

Construction of a regular extension of $ℚ (T)$ with Galois group $M_{24}$ . (Construction d'une extension régulière de $ℚ (T)$ de groupe de Galois $M_{24}$ .)

Delta-composantes des espaces de modules de revêtements

Demuskin Groups of Rank N0 as absolute Galois Groups.

Dessins d'enfants: bipartite maps and Galois groups.

Die Probleme der modernen Galoisschen Theorie.

Differential Galois realization of double covers

Disconnected groups of Lie type as Galois groups.

Einige orthogonale und symplektische Gruppen als Galoisgruppen über Q.

Errata-Corrige : “Some sporadic groups as Galois groups II”

Familles de revêtements de la droite projective

Currently displaying 1 – 20 of 76