AbsoluteGaloisGroup 2002-01-21 22:15:50 2004-03-14 16:53:29 Definition % 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 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 $k$.