Talk:Symmetry group/Archive 1

Archive 1

1

My 2c on this page - it has useful info but could be made more readable and more concrete. Symmetry groups are a great starting point for finding out about finite group theory -- especially the symmetry groups of plane figures and archimedian solids, but this article dives in with "congruencies", "invariant" and "composition". Most non-mathematical readers (including proto-mathematicians) would not survive the first sentence. The link to Group theory doesn't help much either. ... and subheadings would help.

If I get around to it in the next few weeks I will put in a gentler introduction and some examples that will ease the transition into the language of the two and three dimensions sections. I am not a groupie though, so if anyone else has the skills and energy, I will not be offended. AndrewKepert 06:15, 12 November 2003 (UTC)

How about, "The symmetry group of a geometric figure is the set of symmetry operations, such as rotations and reflections, which leave the figure indistinguishable from its original form. For example, a square can be rotated a quarter of a turn, and it is still the same square. It can be also reflected about lines through the center parallel to the edges or passing through opposite corners." --Snags 20:39, 8 October 2004 (UTC)

"Td. This group has the same rotation axes as T, but with six mirror planes, each containing a single C2 axis and four C3 axes." You mean two C3 axes, right? A plane cannot contain all four C3 axes. — Preceding unsigned comment added by 24.21.186.218 (talk) 06:17, 13 June 2005 (UTC)

Request for technical explanation

Probably the best thing to do would be to include a concrete example with diagram(s) in the introduction. (Perhaps what Snags suggests above.) The current introduction gets into a lot of details which are hard to parse, and which should probably be put into subsections. The 1D, 2D, and 3D sections could certainly also use some diagrams or pictures showing concrete examples. -- Beland 17:00, 18 December 2005 (UTC)

editorial templates formerly in article text

(This page currently does not yet describe various aspects of symmetry groups in theoretical physics, especially in (quantum and classical) field theory.)

I agree. Will add a disamibuation link. — Preceding unsigned comment added by Debivort (talk • contribs) 18:34, 6 January 2006 (UTC)

The article has had a link to a DAB page which lists the physics symmetry groups for many months now. Debivort 21:00, 17 January 2007 (UTC)

the case of the comma

The last editor apparently read a book that said i.e. (id est = 'that is') and e.g. (exempli gratia = 'for example') are always followed by a comma. Bad book. If they are followed by a comma, they ought also to be preceded by one; see Parenthesis (rhetoric). But these additions brought my attention to some passages that could be improved, so thanks all the same!

Sometimes a broader concept of "same symmetry type" is used, resulting in[,] e.g., 17 wallpaper groups.

I removed this sentence because I can't make sense of it. Does it mean that wallpaper group is itself a broad symmetry type, and thus all 17 are in a broad sense "the same"? Or that, with a narrower understanding of "same", there would be more than 17 of them? —Tamfang (talk) 06:07, 8 December 2008 (UTC)

Actually, "i.e." and "e.g." are parenthetical, which means that they should be punctuated accordingly. Generally this means following them with a comma and preceded with some other form of punctuation which may or may not be a comma. So I do not agree with the conditional proposition in the above post beginning "If..." siℓℓy rabbit (talk) 13:24, 8 December 2008 (UTC)

We agree that they're parenthetical; the previous editor mechanically added a comma without adding any preceding punctuation, as in the line quoted. —Tamfang (talk) 03:42, 12 December 2008 (UTC)

Merge

I would like to start a discussion to propose the merge o the Symmetric group to this one. Clearly both articles refer to the same concept, despite the fact that the other article states that it focus on "finite sets". --Pedro 20:49, 6 May 2010 (UTC) —Preceding unsigned comment added by Pcgomes (talk • contribs)

I disagree that the two articles refer to the same concept. The symmetric groups are a particular sequence of groups of orders 1, 2, 6, 24, ... . In contrast, all groups are symmetry groups, and symmetry groups exist of all orders. —Mark Dominus (talk) 01:21, 7 May 2010 (UTC)

The symmetric groups are also called permutation groups. They are groups on sets in which the arrangement of any subset is independent of the arrangement of other subets, which is not true of (for example) the vertices of a polyhedron (other than a simplex). —Tamfang (talk) 01:53, 7 May 2010 (UTC)

do not merge - per above. They are separate concepts deserving separate articles. de Bivort 01:57, 7 May 2010 (UTC)

Symmetric groups, permutation groups and symmetry groups are all different concepts. The first notion is absolute (the adjective depends only on the group: a given group with 168 elements (any one) is not a symmetric group, period) but the other two are are relative (the chosen group could be realized as permutation group on some set of elements, or as symmetry group of some configuration, both of which would need to be specified for the statement to make sense). Merging the articles would be a blunder, reinforcing the confusion possibly caused by the terminology. Marc van Leeuwen (talk) 04:51, 7 May 2010 (UTC)

Fundamental mistake in introductory sentences

The first two sentences of this article are as follows:

"In abstract algebra, the symmetry group of an object (image, signal, etc.) is the group of all isometries under which the object is invariant with composition as the operation. It is a subgroup of the isometry group of the space concerned."

There is no reason in the world for an object to have a "space concerned".

Also there are many symmetry groups of objects that are not metric spaces, so the symmetry group has nothing to do with preserving distances. It would be a group that preserves some property.

For example: The symmetry group of a set is just all permutations of elements of the set. The symmetry group of a Riemann surface is the group of conformal transformations of the surface. The symmetry group of a topological space is its group of self-homeomorphisms. The symmetry group of a group is its group of automorphisms.

In general, the symmetry group of any mathematical structure is the group of invertible self-mappings that preserve that structure.Daqu (talk) 20:29, 20 June 2015 (UTC)

I disagree that the space has nothing to do with it. The space is the mathematical object affects the size of the group of an embedded object's symmetries.

I agree with your remaining statements. The concept of a symmetry group relates to he preservation of chosen properties, and isometry is specific to a space with a metric. We should remove the isometry-centric assumption. —Quondum 21:02, 20 June 2015 (UTC)

Daqu comes close to what I have seen as "good" definitions in the literature. Permit the structure "no structure", except the set itself (permutation group) and a symmetry group of a structure on a set is a subgroup of the permutation group preserving that structure on that set. I don't think it is necessary to include "images" and "signals" explicitly, they are represented as sets. Can't remember exactly from where I got this. The definition we give must absolutely be referenced. YohanN7 (talk) 20:18, 15 July 2015 (UTC)