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:
Public domain 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.

Licensing

Public domain 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.

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current04:10, 14 November 2008Thumbnail for version as of 04:10, 14 November 2008284 × 278 (32 KB)wikimediacommons>Michael K. Edwards{{Information |Description= |Source= |Date= |Author= |Permission= |other_versions= }}

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