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'absolute Galois group'
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| Title of object: |
absolute Galois group |
| Canonical Name: |
AbsoluteGaloisGroup |
| Type: |
Definition |
| Created on: |
2002-01-21 22:15:50 |
| Modified on: |
2002-05-21 08:31:51 |
| Classification: |
msc:12F10 |
Preamble:
% this is the default PlanetMath preamble. as your knowledge
% of TeX increases, you will probably want to edit this, but
% it should be fine as is for beginners.
% almost certainly you want these
\usepackage{amssymb}
\usepackage{amsmath}
\usepackage{amsfonts}
% used for TeXing text within eps files
%\usepackage{psfrag}
% need this for including graphics (\includegraphics)
%\usepackage{graphicx}
% for neatly defining theorems and propositions
%\usepackage{amsthm}
% making logically defined graphics
%\usepackage{xypic}
% there are many more packages, add them here as you need them
% define commands here |
Content:
| Let $k$ be a field. The {\em absolute Galois group} $G_k$ of $k$ is the Galois group $\operatorname{Gal}(k^{\operatorname{sep}}/k)$ of the field extension $k^{\operatorname{sep}}/k$, where $k^\operatorname{sep}$ is the separable closure of $k$. |
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