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File:Symmetric group 4; Cayley table; numbers.svg




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This is a file from the Wikimedia Commons

From Wikipedia, the free encyclopedia
  

●File
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●Metadata
 File:Symmetric group 4; Cayley table; numbers.svg
Size of this PNG preview of this SVG file: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels | 744 × 744 pixels.

Original file ‎(SVG file, nominally 744 × 744 pixels, file size: 1.31 MB)





Summary

Description
A submatrix containing all 24 elements

Cayley table of the symmetric group S4 showing all 24 permutations of 4 elements

There is also:
left action
last ⋅ first
This is:
right action
first ⋅ last

For left action (the usual way to compose functions) see: File:Symmetric group 4; Cayley table (left); numbers.svg

Even permutations are white:

Odd permutations are colored:

  • six transpositions (green)
  • six 4-cycles (orange)

Calculation of the matrix with Python: http://pastebin.com/BGkvfdgH

This SVG was created with Inkscape.
Date
Source Own work
Author
Watchduck
You can name the author as "T. Piesk", "Tilman Piesk" or "Watchduck".

Licensing

I, the copyright holder of this work, hereby publish it under the following licenses:
GNU head Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.
w:en:Creative Commons
attribution
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
You are free:
  • to share – to copy, distribute and transmit the work
  • to remix – to adapt the work
    • Under the following conditions:
    • attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
    You may select the license of your choice.

    Captions

    Add a one-line explanation of what this file represents

    Items portrayed in this file

    depicts

    some value

    author name string: Watchduck
    Wikimedia username: Watchduck
    URL: http://commons.wikimedia.org/wiki/User:Watchduck

    copyrighted

    GNU Free Documentation License, version 1.2 or later

    Creative Commons Attribution 3.0 Unported

    original creation by uploader

    2010

    File history



    Click on a date/time to view the file as it appeared at that time.
    Date/TimeThumbnailDimensionsUserComment
    current21:50, 10 May 2017Thumbnail for version as of 21:50, 10 May 2017744 × 744 (1.31 MB)Watchduckactive right matrices
    11:08, 16 October 2014Thumbnail for version as of 11:08, 16 October 2014744 × 744 (1.32 MB)Wereldburger758Valid SVG now.
    21:02, 2 March 2011Thumbnail for version as of 21:02, 2 March 2011744 × 744 (1.39 MB)Watchduckbackwards notation
    16:01, 2 August 2010Thumbnail for version as of 16:01, 2 August 2010744 × 744 (1.7 MB)Watchduck{{Information |Description=Cayley table of the symmetric group S<sub>4</sub> All permutations of 4 elements, or the tetrahedron respectively |Source={{own}} |Date= |Author=[[User:Lipedia|Lipedia]



    The following pages on the English Wikipedia use this file (pages on other projects are not listed):
    ●Alternating group
    ●Subgroup

    Global file usage


    The following other wikis use this file:

    ●Usage on en.wikiversity.org

    ●Symmetric group S4
    ●Permutation notation

    ●Usage on gl.wikipedia.org

    ●Subgrupo

    ●Usage on hu.wikipedia.org

    ●Részcsoport

    ●Usage on id.wikipedia.org

    ●Subgrup
    ●Grup selang-seling

    ●Usage on it.wikipedia.org

    ●Utente:Grasso Luigi/sandbox4/Gruppo alterno

    ●Usage on ko.wikipedia.org

    ●부분군

    ●Usage on no.wikipedia.org

    ●Gruppeteori

    ●Usage on sl.wikipedia.org

    ●Podgrupa

    ●Usage on sv.wikipedia.org

    ●Alternerande grupp

    ●Usage on ta.wikipedia.org

    ●உட்குலம் (கணிதம்)


    Metadata

    This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.

    If the file has been modified from its original state, some details may not fully reflect the modified file.


    Retrieved from "https://en.wikipedia.org/wiki/File:Symmetric_group_4;_Cayley_table;_numbers.svg"






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