Odd parts of tame kernels of dihedral extensions
On dihedral algebraic function fields
On finite linear groups stable under Galois operation.
On Geometric Embedding Problems and Semiabelian Groups.
On Grunwald-Wang's theorem.
On Hopf Galois structures and complete groups.
On Ideal Theory in High Prufer Domains.
On irreducible components of a Weierstrass-type variety
We give a characterization of the irreducible components of a Weierstrass-type (W-type) analytic (resp. algebraic, Nash) variety in terms of the orbits of a Galois group associated in a natural way to this variety. Since every irreducible variety of pure dimension is (locally) a component of a W-type variety, this description may be applied to any such variety.
On nilpotent Galois groups and the scope of the norm limitation theorem in one-dimensional abstract local class field theory.
On normal binomials
On realizability of p-groups as Galois groups
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 topics.
On Relations Between Zeros of Galois Polynomials.
On relative integral bases for unramified extensions
0. Introduction. Since ℤ is a principal ideal domain, every finitely generated torsion-free ℤ-module has a finite ℤ-basis; in particular, any fractional ideal in a number field has an "integral basis". However, if K is an arbitrary number field the ring of integers, A, of K is a Dedekind domain but not necessarily a principal ideal domain. If L/K is a finite extension of number fields, then the fractional ideals of L are finitely generated and torsion-free (or, equivalently, finitely generated and...
On Solvability by Radicals of Field Extensions.
On Solvability by Radicals of Finite Fields.
On the class numbers of certain Hilbert class fields.
On the compositum of all degree extensions of a number field
We study the compositum of all degree extensions of a number field in a fixed algebraic closure. We show contains all subextensions of degree less than if and only if . We prove that for there is no bound on the degree of elements required to generate finite subextensions of . Restricting to Galois subextensions, we prove such a bound does not exist under certain conditions on divisors of , but that one can take when is prime. This question was inspired by work of Bombieri and...
On the computation of resolvents and Galois groups.
On the Computation of the Galois Group over the Quotient Field of C [...].
On the Construction of Galois Extensions of Function Fields and Number Fields.