Template talk:Group theory sidebar

Infinite Groups

The groups of conformal symmetries on a string worldsheet and the groups of symmetries of metric transformations in General relativity need to be added here somehow.

Image

This image has a transparent background. For browsers that don't (fully) support SVG, it is converted into a PNG image, with transparent white blackground. Unfortunately some older programs, including Microsoft Paint and my printer driver, render all transparent PNG backgrounds as black. This problem could be solved by uploading an alternative version of this image with white background. But before doing this I would like to ask another question.

Does anyone else think this image isn't a good illustration for the topic "groups"? I think it's not even obvious that this is supposed to be a polytope, and much less that we are interested in its symmetries. I think the image of Rubik's cube that is currently on group (mathematics) would do a much better job here. Would that be an acceptable replacement? --Hans Adler (talk) 10:02, 29 April 2008 (UTC)

I think the usefulness of an illustration of an abstract concept is heavily dependent on its context. In particular, I find it hard to believe there is any worthwhile picture that can be put on a general use template. It is easy to use illustrations to compare and contrast two abstract notions (for instance see the introduction to Khukhro's book on automorphisms of p-groups for lovely pictures).

It is virtually impossible to picture a group, since a group *acts*. One could use an animation to illustrate the action, but I think many would object to an animated infobox. Since we cannot illustrate the action, we instead illustrate the thing upon which the group acts. No such picture can adequately describe the group. The wireframe polytope conveys no notion of symmetry group at all, but neither does a picture of the rubik's cube (though I will admit it does a slightly better job, since it is "caught in the act" of turning).

Another poor possibility is to illustrate a hyperbolic reflection group with a quaint little arrow pointing from one fundamental domain to another. Using the disk model you can have a very pretty picture of a place where a group acts, and the picture can be sufficiently decorated to indicate completely the action of one or perhaps even two reflections.

Practically, yes, I think replacing the polytope by the Rubik's cube is likely an improvement, though not a huge one. JackSchmidt (talk) 14:07, 29 April 2008 (UTC)

I added a bit of template trickiness. I wanted to add the Groups template to the Groups article but it already has its own Rubik's Cube image. So the image now has parameter name, image_param. In the Groups article, image_param=. This means the image parameter becomes nothing and no Rubik's Cube. Anyways, it works and it shouldn't break any other articles.--Olsonist (talk) 21:01, 9 April 2012 (UTC)

Euclid's orchard is not a good image to illustrate the general concept of groups. Can somebody come up with a more relevant image? I changed it to the cyclic group Z/6Z. If others feel this is a bad choice, feel free to revert. Perhaps the template does not need an image.--Foobarnix (talk) 19:49, 16 July 2015 (UTC)

Why not use a Cayley diagram to illustrate groups? It shows group actions quite clearly without the need for animations. Here is an example one File:Dih_4_Cayley_Graph;_generators_a,_b.svg. --Dewitt Sciullo (talk) 20:21, 16 August 2020 (UTC)

Link to Groups is a bad idea

The {{PhysicsNavigation}} template is being misused here. It conflates the Name and Title ideas. Since the template is called Template:Groups the Name parameter has to be "Groups". However, the PhysicsNavigation template expects there to be a main space article of the same name. In this case, Groups is a redirect to a disambig that does not even list the math term in the first page of popups.

In particular, the Title parameter is not used at all (it is ignored), but the title of the little infobox is '''[[{{{Name}}}]]'''. To fix this, I have to do one of the following:

• edit the PhysicsnNavigation template to set the title to '''[[{{{Title|{{{Name}}}}}}]]'''
• copy the PhysicsNavigation to a new template and make the change there
• move this template to something like Template:Group (mathematics)

Anyone have a preference? JackSchmidt (talk) 13:53, 29 April 2008 (UTC)

I'd vote for option 3 but all options seem reasonable. Tassedethe (talk) 09:29, 11 June 2008 (UTC)

Fintie groups

Should the (incomplete) list of sporadic groups really be taking up most of the space in the "finite" section of this template? Maybe just one link to "sporadic groups"? Though I couldn't decide what to put in its place. Also, the template wikicode looked intimidating, so I just did the lazy thing and filed a complaint here instead. --GodMadeTheIntegers (talk) 19:23, 16 April 2015 (UTC)