Orbit 2002-01-21 22:26:46 2003-11-05 17:34:38 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 $G$ be a group, $X$ a set, and $\cdot: G \times X \longrightarrow X$ a group action. For any $x \in X$, the {\em orbit} of $x$ under the group action is the set $$ \{g\cdot x \mid g \in G\} \subset X. $$