On the embedding problem for nonsolvable Galois groups of algebraic number fields: Reduction theorems

On the Embedding Problem for Nonsolvable Galois Groups of Algebraic Number Fields: Reduction Theorems

is to construct an extension L/K such that L/k is Galois, and such that there exists an isomorphism /?:£ -* E, where £ = Gal(L//c), such that y ResL/K = e(i. L is called a solution field, j? a solution isomorphism, and the pair (L, fi) a solution, to P. At times we only require /? to be monomorphic; in such a context (L, /?) is called an improper solution, and if j? is epi, (L, /?) is a proper ...

Procyclic Galois Extensions of Algebraic Number Fields

6 1 Iwasawa’s theory of Zp-extensions 9 1.

Actions of Galois Groups on Invariants of Number Fields

In this paper we investigate the connection between relations among various invariants of number fields L coresponding to subgroups H acting on L and of linear relations among norm idempotents.

Sum-product Theorems in Algebraic Number Fields

Duality Theorems in Galois Cohomology over Number Fields

the direct limit taken over all finite Galois extensions K of k in which the integral closure Y of X is unramified over X, where GKJk denotes the Galois group of such an extension, and where GY denotes the group of points of G with coordinates in Y. For example, if X=k, our notation coincides with that of [10]. For any X, the group H(X,C) is the r-th cohomology group of the profinite group Gjr=...