File:First-isomorphism-theorem.svg

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Summary

Description

English: Commutative diagram, showing the first isomorphism theorem.

Date

13 November 2008 (original upload date)

Source

Created as per: en:meta:Help:Displaying a formula#Commutative diagrams

\documentclass{amsart}
\usepackage[all, ps, dvips]{xy} % Loading the XY-Pic package
                                % Using postscript driver for smoother curves
\usepackage{color}              % For invisible frame
\begin{document}

\newcommand{\im}{\operatorname{im}}
% \newcommand{\stack}[2]{\genfrac{}{}{0pt}{}{#1}{#2}}
\newcommand{\stack}[2]{\underset{#2}{#1}}

\thispagestyle{empty} % No page numbers
\SelectTips{eu}{}     % Euler arrowheads (tips)
\setlength{\fboxsep}{0pt} % Frame box margin
{\color{white}\framebox{{\color{black}$$ % Frame for margin

\xymatrix @=1pt@! { %We want equal spacing, and the entries close together
           &                        & 0 \ar[dr]                   &                                                          & 0\\
           &                        &                             & \stack{G / \ker f}{\cong\;\im f} \ar[ur] \ar[dr]^{\iota} & \\
           &                        & G \ar[rr]^{f} \ar[ur]^{\pi} &                                                          & H\\
           & \ker f \ar[ur]^{\kappa}&                             &                                                          & \\
  0\ar[ur] &                        &                             &                                                          &
}

$$}}} % end math, end frame
\end{document}

Author

Michael K. Edwards

Permission
(Reusing this file)

Michael K. Edwards, the copyright holder of this work, hereby publishes it under the following license:

This work has been released into the public ___domain by its author, Michael K. Edwards. This applies worldwide.
In some countries this may not be legally possible; if so:
Michael K. Edwards grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Licensing

I, the copyright holder of this work, release this work into the public ___domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

File history

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	Date/Time	Dimensions	User	Comment
current	02:10, 14 November 2008	284 × 278 (32 KB)	Michael K. Edwards	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}
	23:45, 13 November 2008	284 × 278 (31 KB)	Michael K. Edwards	{{Information \|Description= \|Source= \|Date= \|Author= \|Permission= \|other_versions= }}
	23:25, 13 November 2008	524 × 438 (32 KB)	Michael K. Edwards	{{Information \|Description={{en\|1=Commutative diagram for the first isomorphism theorem.}} \|Source=Own work by uploader \|Author=Michael K. Edwards \|Date=2008-11-13 \|Permission= \|other_versions= }} <!--{{ImageUpload\|full}}-->