<?xml version="1.0" encoding="UTF-8"?>

<record version="5" id="1114">
 <title>first isomorphism theorem</title>
 <name>FirstIsomorphismTheorem</name>
 <created>2001-12-21 03:27:55</created>
 <modified>2005-05-03 01:39:04</modified>
 <type>Theorem</type>
 <creator id="6075" name="rspuzio"/>
 <author id="6075" name="rspuzio"/>
 <author id="62" name="nerdy2"/>
 <classification>
	<category scheme="msc" code="20A05"/>
	<category scheme="msc" code="13A15"/>
 </classification>
 <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</preamble>
 <content>If $f : G\to H$ is a homomorphism of groups (or rings, or modules), then it induces an isomorphism $G/\ker f \cong {\rm im} f$.</content>
</record>
