An arithmetic proof of Pop`s Theorem concerning Galois groups of function fields over number fields.
An explicit integral polynomial whose splitting field has Galois group
Using the principle that characteristic polynomials of matrices obtained from elements of a reductive group over typically have splitting field with Galois group isomorphic to the Weyl group of , we construct an explicit monic integral polynomial of degree whose splitting field has Galois group the Weyl group of the exceptional group of type .
An isomorphism theorem for Henselian algebraic extensions of valued fields.
Anelli regolari separabilmente chiusi
Annihilating polynomials for quadratic forms.
Arten und Gattungen von Abbildungsgruppen. Ein elementares Beispiel aus der Galoisschen Theorie.
Asymptotics of number fields and the Cohen–Lenstra heuristics
We study the asymptotics conjecture of Malle for dihedral groups of order , where 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
We establish automatic realizations of Galois groups among groups , where is a cyclic group of order for a prime and is a quotient of the group ring .
Automorphism Groups of Algebraic Number Fields.
Automorphism Groups of Fields.