Number fields with solvable Galois groups and small Galois root discriminants

Number fields with solvable Galois groups and small Galois root discriminants

We apply class field theory to compute complete tables of number fields with Galois root discriminant less than 8πeγ . This includes all solvable Galois groups which appear in degree less than 10, groups of order less than 24, and all dihedral groups Dp where p is prime. Many people have studied questions of constructing complete lists of number fields subject to conditions on degree and possib...

Minimal Discriminants for Fields with Small Frobenius Groups as Galois Groups

Galois Groups over Nonrigid Fields

Let F be a field with charF 6= 2. We show that there are two groups of order 32, respectively 64, such that a field F with char F 6= 2 is nonrigid if and only if at least one of the two groups is realizable as a Galois group over F . The realizability of those groups turns out to be equivalent to the realizability of certain quotients (of order 16, respectively 32). Using known results on conne...

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.

Arithmetic of Fields Safarevi C's Theorem on Solvable Groups as Galois Groups I

The organizers of the meeting were Wulf-Dieter Geyer (Erlangen) and Moshe Jarden (Tel Aviv). The 26 talks that were given during the conference fall (roughly) into several categories: 1. Fundamental groups and covers in characteristic p In the rst of two talks on the famous theorem of Safarevi c \Every nite solvable group occurs as a Galois group over a global eld" this result was composed with...