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

From Wikimedia Commons, the free media repository
Jump to navigation Jump to search

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

Captions

Captions

Add a one-line explanation of what this file represents

Summary[edit]

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[edit]

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.

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)Watchduck (talk | contribs)active right matrices
11:08, 16 October 2014Thumbnail for version as of 11:08, 16 October 2014744 × 744 (1.32 MB)Wereldburger758 (talk | contribs)Valid SVG now.
21:02, 2 March 2011Thumbnail for version as of 21:02, 2 March 2011744 × 744 (1.39 MB)Watchduck (talk | contribs)backwards notation
16:01, 2 August 2010Thumbnail for version as of 16:01, 2 August 2010744 × 744 (1.7 MB)Watchduck (talk | contribs){{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]

You cannot overwrite this file.

File usage on other wikis

The following other wikis use this file:

Metadata

This file contains additional information such as Exif metadata which may have been added by the digital camera, scanner, or software program used to create or digitize it. If the file has been modified from its original state, some details such as the timestamp may not fully reflect those of the original file. The timestamp is only as accurate as the clock in the camera, and it may be completely wrong.

Retrieved from "https://commons.wikimedia.org/w/index.php?title=File:Symmetric_group_4;_Cayley_table;_numbers.svg&oldid=512444747"