File:First-isomorphism-theorem.svg

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First-isomorphism-theorem.svg‎ (SVG file, nominally 284 × 278 pixels, file size: 32 KB)

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[edit] Summary

Description

English: Commutative diagram, showing the first isomorphism theorem.

Date

2008-11-13 (first version); 2008-11-13 (last version)

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 image)

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

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

[edit] Licensing:

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
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	Thumbnail	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}}-->)