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Group (mathematics)

Article (edit | visual edit | history) · Article talk (edit | history) · Watch • Watch peer review

This peer review discussion has been closed.
The group article is up to peer review. When reviewing, please note that there is another related article, group theory. The latter is (or shall be) devoted to advanced topics related to groups, whereas the article under review is to cover more basic facets. Merging the two articles has been proposed several times, but consensus was reached not to do so (see for example here).

The article has reached WP:GA status some time ago and has since been expanded somewhat more, so as to include history and more material on applications. I'm also putting this to PR as to see whether there are significant hindrances to a possible FAC, so if you want to comment on that perspective too, please do so.

Thanks in advance for your review, Jakob.scholbach (talk) 19:24, 30 May 2008 (UTC)[reply]


Ruhrfisch comments: I am not a mathematician, although I do know a bit about group theory and symmetry. I was going to ask Geometry guy to review this and see you already have, so here goes. The article looks pretty good to me, most of my edits will be pretty nitpicky:

  • One of my standard peer review tricks is to suggest a model article - I will leave it as an exercise to the reader to decide which, if any of the articles here may be good models.
  • The lead should be a summary of the whole article, an accessible and inviting overview. My rule of thumb is to include every header in the lead in some way - is History in the lead, for example? Please see WP:LEAD
  • The article may need fewer sections / header too
  • Per WP:HEAD do not repeat the title of the article in the headers or use "The" - so "Examples of groups" could just be "Examples". I am not sure the other uses of group can be avoided as headers.
  • I expected there would be a "Second Example" after "First example: the integers" - could it just be "Example: Integers"?
  • This section (first example) needs a reference or two and many other sections seem to as well - My rule of thumb is that every quote, every statistic, every extraordinary claim and every paragraph needs a ref.
  • I liked the article and was able to follow it to about Uniqueness of identity element and inverses. I read further but my brain is tired. One thing to be aware of are avoiding jargon where possible - see WP:JARGON and making sure to provide context for the reader - see WP:PCR. I realize that math articles will generally be written at a level which is beyond most readers, so there are limits these.
  • I will leave it to someone more mathematically talented than I to get into the details of the math. I liked the first two examples very much.

Hope this helps. If my comments are useful, please consider peer reviewing an article, especially one at Wikipedia:Peer review/backlog (which is how I found this article). Yours, Ruhrfisch ><>°° 04:34, 5 June 2008 (UTC)[reply]

  • Hmm, I can't agree with splitting the group and group theory articles based on one being basic and one covering advanced topics. That way the articles are not sticking to their topic, which all articles should. If they are really about the same topic, they should be merged and the one article should carefully follow summary style in order to ease the reader in and present basic information first, with detailed information in subarticles. If instead you are going to treat the articles as different concepts, then the articles need to be very careful about what they cover and not to cover what should be in the other. Currently the article does that. - Taxman Talk 04:57, 5 June 2008 (UTC)[reply]
Many thanks to both of you, Ruhrfisch and Taxman, for your comments. I see from the above, that the (necessary, I believe) separation between groups and their theory needs to be carved out more smoothly and better, and the article is still too technical for a lay reader. These, in addition to the other concerns will be worked on. Jakob.scholbach (talk) 21:36, 5 June 2008 (UTC)[reply]
There are some technical articles that have a simpler Introduction to ... version as well, see Virus and Introduction to virus, for example. Perhaps there could be a simple intro to groups and group theory, then more rigorous articles on each topic. Ruhrfisch ><>°° 01:44, 6 June 2008 (UTC)[reply]
Wow, is that really a consensus idea? The policy for a long time had been that isn't a good idea. I see there other places it has been done, but I personally think it amounts to Wikipedia:Content forking. To my mind, basically all wikipedia articles should be targeted to be easier to understand, especially the main article, then more difficult material should be in properly organized subarticles ala summary style. - Taxman Talk 12:37, 6 June 2008 (UTC)[reply]
Hm. I don't know about policies, but at this time I don't want to write another (even) more introductory article. I'm trying to make everything as easy and understandable as possible, which I had not focussed that much yet. Jakob.scholbach (talk) 20:28, 6 June 2008 (UTC)[reply]

RJH comments:

  • The symmetry group example seems to conflict with the earlier definition, or else it is written in a confusing style. It says that the "elements of the group are operations". Therefore the operations are the members of the set. Then what are the group operations on the set? Is the functional composition supposed to be the binary operation?
  • I'm concerned that this article does not satisfy Wikipedia:Explain jargon. Much of the content assumes pre-existing knowledge that may not be available to the average reader. (See especially the History section.) There is also mathematical nomenclature that may not be clear to all (ex: '∈' in Subgroups.)

—RJH (talk) 15:54, 6 June 2008 (UTC)[reply]

Thanks, RJH! 1) The geometric operations are the same as the elements. I'll have to clarify this. 2) As mentioned above, I'm currently trying to avoid / to introduce well any jargon used. It is impossible to avoid any notion or notation that might not be known by every reader, but a hatnote deferring to mathematical notation and additional wikilinks + explanations should do the job. Jakob.scholbach (talk) 20:28, 6 June 2008 (UTC)[reply]

Markus Poessel has a good impression of the article, overall, and a few comments:

  • Is there a reason for not using templates like template:main or template:see also, but instead using boldfaced wikilinks for subgroup, symmetry, Lie group and the like? I think using the templates would be more in line with the rest of Wikipedia works. For all I know, it could be part of the MOS, but even if it were not, it would be advisable for reasons of consistency.
  • Lead: The first paragraph should give some plain-language description of what a group actually is, not just say that it is an object of study in some particular branch of mathematics. Adding a sentence to that effect would also make sure the first paragraph isn't a one-sentence-paragraph any more.
  • "The wished for existence of a multiplicative inverse of 2 suggests considering the rational numbers Q, the set of all fractions of integers a/b, where a and b are integers and b is nonzero." - that could be put more clearly. Also, should be wished-for.
  • Representation theory: "It deals with the question which spaces a given group acts on." - sounds strange to me. Isn't it more like "which spaces a given group can be made to act on"?
  • "More involved Lie groups are used in physics. Noether's theorem links continuous symmetries to conserved quantities. For example, the Poincaré group plays a pivotal role in special relativity, and quantum field theory.[60] Symmetries are likewise central to gauge theory.[61]" - this makes it sound like the Poincare group playing a pivotal role in special relativity is an example of Noether's theorem. The Noether sentence should probably go last. All in all, I think this description is too short to be of much use to anyone who doesn't know the subject already. Local groups should probably at least get a brief mention, too.
  • I wonder if there's a better way to structure Examples and Applications - should the applications get their own section, with a nice image of x-ray crystallography or whatever?

Markus Poessel (talk) 16:39, 10 June 2008 (UTC)[reply]

Thank you much, Markus.
Ad 1) There is no particular reason, only that I like it better this way. The templates tend to catch up space and attention, so why not linking the key words in the subsection itself? I bolded them to make them more stand out more clearly.
2 (Lead) and 3 (clarity) and 4 (representations) OK, I'll do that
5) Would you be willing to help out at this point? Frankly, I have very little knowledge in these fancy physics stuff. I just asked at the WP:Phys and got roughly this as an answer. By local groups, do you mean local groups? (From a quick scan of the article I can't see why they have any connection with our tiny little nice groups here).
6) Examples and applications section: Actually, a reviewer above asked to reduce the total number of sections. After thinking over it I decided to merge the (previously split) examples and apps sections. As it is, any application uses a particular kind of group, and the other way round, too. So, the two aspects are somewhat entangled. At this point, I would not want to (re)separate the sections.
6b) If you have a nice image of x-ray crystallography, which clearly shows a link to groups, I'd be more than happy to include it. Do you? Or of any other "real-world" application (The images in x-ray crystallography don't seem to meet this wish. Just putting some image of an application like this seems to just clutter up the article). Jakob.scholbach (talk) 18:12, 10 June 2008 (UTC)[reply]
You're welcome.
ad 1) Wikipedia:Summary_style doesn't seem to provide for your version, which would strongly suggest to use Template:main and that, if you intend to bring this article to FA status, that is sure to be one of the objections. Also keep in mind that any bot readings (e.g. for automatic determination how many articles are split, or for a hierarchical map of Wikipedia) are unlikely to pick up on your way of doing things.
ad 5) So much Wikipedia, so little time! But yes, I'll give it a try. And no, by local groups I meant local symmetries - like the gauge symmetries you briefly mentioned.
ad 6) Hm. Of course each application would involve a particular group, but I still think that giving the examples first, and a summary section on applications later would be better.
ad 6b) I can't find the images I'm looking for, either, but under http://commons.wikimedia.org/wiki/Category:Crystal_structures there are many nice crystal symmetries which should serve.

Markus Poessel (talk) 19:35, 10 June 2008 (UTC)[reply]

1) OK. I changed this. The bot argument convinces me. Jakob.scholbach (talk) 21:32, 10 June 2008 (UTC)[reply]

Comments from Ealdgyth (talk · contribs)

  • You said you wanted to know what to work on before taking to FAC, so I looked at the sourcing and referencing with that in mind. I reviewed the article's sources as I would at FAC.
    • Some of your references are lacking page numbers. Specifically I'm thinking of the Wussing book, it's 336 pages according to Google, that's a LOT of searching for sourced information (current ref 5 just is to that book). Other examples might be the Mac Lane reference (current ref 17) or the Kurzweil and Stellmacher ref (current ref 46).
    • You have a citation needed tag on current ref 67. Need to resolve that issue.
Hope this helps. Please note that I don't watchlist Peer Reviews I've done. If you have a question about something, you'll have to drop a note on my talk page to get my attention. (My watchlist is already WAY too long, adding peer reviews would make things much worse.) 22:56, 15 June 2008 (UTC)
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