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'identity element'
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| Title of object: |
identity element |
| Canonical Name: |
IdentityElement |
| Type: |
Definition |
| Created on: |
2002-06-27 19:18:27.621534-04 |
| Modified on: |
2002-06-28 06:05:11.460318-04 |
| Classification: |
msc:20A05 |
| Synonyms: |
identity element=neutral element |
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:
| An \emph{identity element} is an element, traditionally represented by the letter $e$, of a group $G$ such that $ge=eg=g$ for any $g\in G$. The identity element is unique for any given group, and its existence is guaranteed by the definition of a group. |
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