File:First isomorphism theorem (plain).svg

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First_isomorphism_theorem_(plain).svg‎ (SVG file, nominally 113 × 80 pixels, file size: 21 KB)

[edit] LaTeX source

\documentclass{amsart}
\usepackage{amsmath,amssymb,nopageno}
\usepackage[all]{xy}
\DeclareMathOperator{\Ker}{ker}
\begin{document}
 \begin{equation*}
  \xymatrix@C+1em@R+1em{
   G \ar[r]^-{f} \ar[d]_-{\pi} & H \\
   G/\Ker(f) \ar@{-->}[ur]_-{\tilde{f}}
  }
 \end{equation*}
\end{document}

[edit] Summary

Description

The commutative diagram expressing the "first isomorphism theorem". It does not indicate which arrows are injective or surjective.
Date

14 January 2009(2009-01-14)
Source

I created this work entirely by myself.
Author

Ryan Reich (talk)
Permission
(Reusing this image)		 See below.
Other versions w:File:First isomorphism theorem (plain).svg, File:First isomorphism theorem.png

[edit] Licensing

Public domain 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.

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File history

Click on a date/time to view the file as it appeared at that time.

Date/TimeThumbnailDimensionsUserComment
current05:42, 14 January 2009Thumbnail for version as of 05:42, 14 January 2009113×80 (21 KB)Ryan Reich (Talk | contribs) (== LaTeX source == <pre> \documentclass{amsart} \usepackage{amsmath,amssymb,nopageno} \usepackage[all]{xy} \DeclareMathOperator{\Ker}{ker} \begin{document} \begin{equation*} \xymatrix@C+1em@R+1em{ G \ar[r]^-{f} \ar[d]_-{\pi} & H \\ G/\Ker(f) \ar@)

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