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Archive 5Archive 6Archive 7Archive 8

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I concerned that this article no longer meets the FA criteria. The are large sections of uncited text. Can this be resolved without a formal review? --Graham Beards (talk) 11:09, 20 April 2021 (UTC)

What sections, specifically, do you think require additional citation? Ozob (talk) 04:05, 26 April 2021 (UTC)
At least every paragraph.--Graham Beards (talk) 06:46, 26 April 2021 (UTC)
So, to be clear, this is a purely mechanical and syntactic imposition, completely divorced from any understanding of the content? It would be satisfied if we found a basic textbook on group theory and tacked it on as a footnote at the end of every paragraph? You do notice that the FA requirements emphasize that citations are needed "where appropriate", with a link that points to Wikipedia:When to cite, right? See in particular the "Subject-specific common knowledge" bullet point at that link. —David Eppstein (talk) 06:50, 26 April 2021 (UTC)
I'll nominate for WP:FAR and let the community decide.--Graham Beards (talk) 07:52, 26 April 2021 (UTC)
To me this comes across as "I don't want to answer that so I'm going to do the most hostile thing I can". —David Eppstein (talk) 16:32, 26 April 2021 (UTC)
You are mistaken. I chose not to answer your rude assertion about my understanding.--Graham Beards (talk) 16:36, 26 April 2021 (UTC)

This is an article that will have many paragraphs that fall squarely under the Subject-specific common knowledge, so we will need a list of sentences that need citations. From a quick read, it seems the article has very good bones, and it shouldn't take much time to bring it up to modern FA standards. A few points of improvement

  • Standard Model not mentioned in the body
This seems to have been done by someone else already. Jakob.scholbach (talk) 09:42, 30 April 2021 (UTC)
  • footnote a is a bit outdated, and is used to support that group theory impacts other fields, which isn't immediately clear
I have updated it to 2020. In my understanding this is used to support that group theory is an active mathematical discpline, not how it impacts other fields. For that purpose this note is perfectly appropriate, IMO. Jakob.scholbach (talk) 10:53, 2 May 2021 (UTC)
Ah, now I see it is used a second time. Jakob.scholbach (talk) 11:04, 2 May 2021 (UTC)
I've tweaked the article so that footnote is only used once, and now we point to the "Examples and applications" section to show how group theory has applications. XOR'easter (talk) 21:02, 2 May 2021 (UTC)
  • In the rightmost example below: with people reading on phones, this should be phrased differently (last example? May be too unclear)
Sorry, what is your objection here? Jakob.scholbach (talk)
this one also has been taken care of :). FemkeMilene (talk) 19:28, 30 April 2021 (UTC)

Citations:

  • Research is ongoing to simplify the proof of this classification -> cited to a 2004 study
Included a more up-to-date reference. Jakob.scholbach (talk) 19:11, 2 May 2021 (UTC)
  • Kernel and image of group homomorphisms and the first isomorphism theorem address this phenomenon .. cn?
I don't think this needs a citation: the kernel is the identity element if and only if a homomorphism is injective (see the subarticle). This is domain-specific standard knowledge, IMO. Jakob.scholbach (talk) 09:49, 30 April 2021 (UTC)
  • I think some of the footnotes need citations: g, j, p
Done for j. Jakob.scholbach (talk) 09:42, 30 April 2021 (UTC)
Done for p. Jakob.scholbach (talk) 17:13, 30 April 2021 (UTC)
Done for g. XOR'easter (talk) 20:47, 2 May 2021 (UTC)
  • The problem can be dealt with ... cn?
I am not convinced this needs a specific citation. Basically you could name any (contemporary) book on Galois theory (such as the ones we do cite above). Jakob.scholbach (talk) 09:49, 30 April 2021 (UTC)
But Galois theory isn't standard knowledge for laypeople with a keen interest in mathematics (I quote Wikipedia:When to cite: Subject-specific common knowledge: Material that someone familiar with a topic, including laypersons, recognizes as true. Example (from Processor): "In a computer, the processor is the component that executes instructions."). Can it be found in simpler sources too? FemkeMilene (talk) 16:13, 3 May 2021 (UTC)
I added a citation to a textbook chapter. XOR'easter (talk) 03:35, 4 May 2021 (UTC)
  • A presentation of a group can also be used to construct the Cayley graph .. cn?
Citation added. XOR'easter (talk) 20:35, 2 May 2021 (UTC)
I added the Standard Model to an appropriate spot in the body text and rephrased the rightmost example line. XOR'easter (talk) 21:47, 26 April 2021 (UTC)
  • Please add alt text to images for accessibility
Done. Jakob.scholbach (talk) 10:53, 2 May 2021 (UTC)
Done for those where (IMO) the nuisance of the link outweighs the benefits. If you see some more that you specifically think should go, please let me know. Jakob.scholbach (talk) 09:42, 30 April 2021 (UTC)
I've removed a few more. Hope that works. FemkeMilene (talk) 19:35, 30 April 2021 (UTC)

Thanks, Femkemilene for your comments. I have addressed some of them and will work on the remainder asap. Jakob.scholbach (talk) 09:42, 30 April 2021 (UTC)

Brilliant, thanks for your swift work! FemkeMilene (talk) 16:13, 3 May 2021 (UTC)

Comments from my second read:

  • The last sentence of the first paragraph of the lede is difficult to understand. I'm not sure whether splitting it in two is sufficient.
OK, I have rephrased this. Jakob.scholbach (talk) 18:50, 3 May 2021 (UTC)
I still find it too difficult, which is a disservice to the rest of the article. I'm unfortunately not great with prose, but I see two problems with "While these are familiar from many mathematical structures, such as number systems—for example, the integers endowed with the addition operation form a group—the formulation of the axioms is detached from the concrete nature of the group and its operation."
1. such as and for example is quick succession makes it more difficult to read. I think leaving out "such as number systems" works, considering that "number systems" may not be familiar to everybody reading this. I can guess what it means, but not sure.
2. the formulation of the axioms is detached from the concrete nature of the group and its operation. Not entirely sure what this is meant to say. FemkeMilene (talk) 19:06, 3 May 2021 (UTC)
Re 1. I have broken the sentence into two. I think leaving out number systems makes the lead less informative. The directly following example of the integers should convey enough implicit meaning about number systems to be OK here.
Re 2: this is meant to say that the group axioms don't make reference to the nature of the group elements, nor to "what" the group operation actually is. This is a critical piece of information. If you have a better way of saying this, let me know! Jakob.scholbach (talk) 20:51, 4 May 2021 (UTC)
David Eppstein, could I have a third opinion here? I know a lot of your work is comprehensible, so wonder whether you can simplify or assure me it does not need simplifying. FemkeMilene (talk) 20:20, 7 May 2021 (UTC)
Re 2, it might help to figure out what the concept to be conveyed here is. It could be that you can have groups in various contexts (e.g. S3 acting on {a,b,c} or {1,2,3} are both groups) or that all isomorphic groups are the same group (e.g. S3 acting on {a,b,c} or {1,2,3} are the same group). Or that everything that satisfies the axioms is a group (which it really seems to be saying), but that is kinda too implicit in the idea of what axioms are for to be using such abstruse language. If the latter, wouldn't "Any set and operation that satisfies the axioms is a group" be clearer? —Quondum 20:54, 7 May 2021 (UTC)
I just came across this page, and came here to say that this sentence is very confusing to me (I am mathematician, familiar with groups, group actions, group representations, etc). Whatever exactly it is supposed to mean (Jakob.scholbach's explanation above did not clarify it for me), it seems it has to be an improperly constructed sentence: according to my reading it seems to implicitly suggest that the "concrete nature of the group and its operation" (I don't know what this means) has some manner of existence prior to the "formulation" (?) of the axioms. I assume we all agree that the opposite is the case. Gumshoe2 (talk) 05:57, 15 February 2022 (UTC)
This is regarding the two sentences "The formulation of the axioms is, however, detached from the concrete nature of the group and its operation. This allows one to handle entities of very different mathematical origins in a flexible way, while retaining essential structural aspects of many mathematical objects.", right? Material in the lead is supposed to be a summary of something. I suspect this is (or should be) thought of as a summary of the 19th-century notion of a group touched on in the History section and in more detail in History of group theory, from a time when groups were thought of in some specific formulation of what their elements should be and how they would combine (permutations and composition of permutations) rather than as anything obeying an abstract system of axioms. It's saying that the axiomatic point of view was an improvement because it allowed us to apply group theory more widely in a less cumbersome way rather than having to repeatedly translate one kind of group to another kind of group or re-prove the same theorems for every different kind of group. But if that's the intention, I don't think it expresses it very clearly. —David Eppstein (talk) 06:20, 15 February 2022 (UTC)
Yes, that would make sense and would be good to communicate. It seems a little tricky to formulate clearly in an lead-appropriate way, unfortunately I don't have any good suggestion. Gumshoe2 (talk) 06:27, 15 February 2022 (UTC)
  • Should the quote from Borcherds be moved down? Those technical terms have not been introduced yet
It is true that the monster simple group has not introduced there (and is hardly introduced further down), but Borcherd's description "a huge and extraordinary mathematical object" strikes me as highly appropriate for a layman to grasp a bit of the depth out there... Other than that the quote talks just about the simplicity of these axioms, which is what this § is all about. I suggest leaving it there. Jakob.scholbach (talk) 18:50, 3 May 2021 (UTC)
  • group table at the right -> check throughout for statements like this that don't make sense on phones (where that image is above the text). The majority of our readers now use mobile devices.
Done. Jakob.scholbach (talk) 18:50, 3 May 2021 (UTC)
Found one more: if the hour hand is on 9 and is advanced 4 hours, it ends up on 1, as shown at the right. FemkeMilene (talk) 20:21, 7 May 2021 (UTC)
Fixed. Jakob.scholbach (talk) 13:03, 8 May 2021 (UTC)
  • For example, group theory is used to show that optical transitions between certain quantum levels cannot occur simply because of the symmetry of the states involved. cn
This is one of those things that's probably stated in some form in just about any intermediate quantum-physics book. I've added an older reference that I had at hand, and I'll poke around for a more recent one that seems particularly good. XOR'easter (talk) 23:56, 3 May 2021 (UTC)
  • For example, an element of the (2,3,7) triangle group acts on a triangular tiling of the hyperbolic plane by permuting the triangles, cn
Done. —David Eppstein (talk) 03:53, 4 May 2021 (UTC)
  • though the double bonds reduce this to pyritohedral symmetry, cn
I removed this second half of the sentence, none of the sources I looked at mentioned that. Added a ref. Jakob.scholbach (talk) 18:07, 7 May 2021 (UTC)
  • rest of these images probs also need citations (mentioned above, but XOR'Easter's (brilliant name) response directly below may have caused confusion )
Added references. I pinged WP Chemistry about the JT-effect, will add one there, too. Jakob.scholbach (talk) 18:07, 7 May 2021 (UTC)
  • the category of groups: I think this entire section is quite difficult, and uses terms that an applied mathematician won't be familiar with. I don't think it falls under domain-specific common knowledge. Can it be slightly simplified (what is a category?) and cited?
I decided to trim this § down to a sentence which is now placed in the paragraph on homomorphisms. Elaborating on the notion of a category is IMO better left to articles where this has a stronger effect (e.g., for abelian groups). Jakob.scholbach (talk) 18:50, 3 May 2021 (UTC)
  • footnote q needs updating
Why? The GAP small groups lists still the same number? Jakob.scholbach (talk) 18:50, 3 May 2021 (UTC)
I think I may have misinterpreted what it says. So I was thinking, does a more modern source have "The groups of order at most 3000 are known"? From your comments it seems like there is a specific collection of groups, called the GAP small groups? Can that be clarified? FemkeMilene (talk) 19:12, 3 May 2021 (UTC)
GAP is software for doing group theory. It includes implementations of all groups of small order. I'm not clear on why this footnote would need updating; once the exhaustive search was done, it's done. XOR'easter (talk) 23:49, 3 May 2021 (UTC)
Yes, the list of groups of order <= 2000 is complete (and the result is in a sense independent of who does it). GAP does not offer a list of groups of order up to 3000, as far as I have seen. Nor does any other site (according to a search I did the other day). In this sense, the citation is still up to date. Jakob.scholbach (talk) 06:54, 4 May 2021 (UTC)
The wording still implies that group 2001 is unknown. Could it be reworded as: "Up to isomorphism, there are about 49 billion groups of order below or equal to 2000", or something in that sense? FemkeMilene (talk) 20:25, 7 May 2021 (UTC)
I have reworded it slightly, but yes, in some sense it is true that groups of order 2001 (not the 2001st group though, this makes no sense) are "unknown" in the sense that there is (to the best of my knowledge) no list available listing them all. Jakob.scholbach (talk) 13:03, 8 May 2021 (UTC)
  • a problem too hard to be solved in general (footnote r), needs updating?
Hm, this is a case where some problem is super-hard, and is known to be super-hard to anyone studying this. Therefore, researchers seem not to restate this too frequently again. At least I didn't find a more recent source for that. Jakob.scholbach (talk) 18:50, 3 May 2021 (UTC)
Thanks for trying. FemkeMilene (talk) 19:13, 3 May 2021 (UTC)

FemkeMilene (talk) 16:13, 3 May 2021 (UTC)

It is referenced when talking about symmetry of Ammonia. Jakob.scholbach (talk) 13:03, 8 May 2021 (UTC)

HF

Barging in here, from the FAR, if that's okay. I've never been taught group theory, so please bear with me when I say stupid things here.

MOS allows for italics for emphasizing things. Since associativity is such an important piece of this concept I believe it is worth highlighting it. Generally my feeling is that italicization is not used too excessively. Jakob.scholbach (talk) 13:03, 8 May 2021 (UTC)
  • Do It is generally preferred for computing with groups and for computer-aided proofs. and It is also useful for talking of properties of the inverse operation, as needed for defining topological groups and group objects. need references?
I have moved this § down to topological groups and added a ref for the second sentence you are asking about. I will check for the first later. Jakob.scholbach (talk) 13:03, 8 May 2021 (UTC)
I think having 1700 scientific papers published per year in some domain is quite aptly proving that this domain is active, no? I see absolutely no problem with this claim. Jakob.scholbach (talk) 13:06, 8 May 2021 (UTC)
I am uncomfortable with this on two levels. One: a high level of interpretation and judgement is needed to (a) classify papers and (b) to translate the number into a conclusion of how "active" the field is. In short, it is WP:SYNTH of the worst kind, even if you will not get many people disagreeing with the conclusion. It invites the query from a reader: "Are you sure?" Two: the number itself needs citation. It should not be claimed out of the blue. —Quondum 13:52, 8 May 2021 (UTC)
In all respect, I think the edit you made indicates that you are not very familiar with the situation here: Math Reviews is not a journal (as you wrote), but rather a service provided by the American Math Society (one of the, if not the most prestigious national mathematical societies). It lists all mathematical papers that have been peer-reviewed, contains secondary reviews of these papers, and contains their classifications into the several areas of maths. This information is in no way a synthesis of other knowledge that has been partly assembled here and there, it is simply a number that is out there. Questioning that 1700+ papers indicates a high level of activity strikes me as being a bit off.
Finally about 2): of course we can include a link to the Mathscinet page, but I frankly don't quite see the need for that. It is (to anyone with a subscription to MSN) a trivially verifiable information. Jakob.scholbach (talk) 12:28, 9 May 2021 (UTC)
You are presumably referring to this edit. I took that it is described as a journal from the linked article Mathematical Reviews. Perhaps, since I lack the necessary familiarity, you should edit the description in both places?
And I am not questioning that it is a high level of activity; I am looking at it from the perspective of a non-mathematician reading this: How does one get a sense of what the figure means when one has no reference, other than the claim made in WP's voice? In non-technical contexts and for schoolgoers, that might seem like a tiny number or an enormous number. Also, to cite the issue and page number that provides the mentioned list would not be strange. —Quondum 16:13, 9 May 2021 (UTC)
Relatedly, although it is correct that Mathematical Reviews was a journal (of reviews), it stopped being published as a journal well before the date given in the note, and became a database, under the different name MathSciNet. I have corrected the note to reflect its name as of the referred-to date. —David Eppstein (talk) 19:42, 9 May 2021 (UTC)
I have included a link to the MSN page (again, there are no issues / page numbers, this is an electronic database). I continue to see absolutely no problem with taking a number of 1700+ papers as an indication that this branch is highly active. If that number wouldn't make it so evidently clear that it is a highly active branch, it would require us to give further references, but this is not the case here. Jakob.scholbach (talk) 20:04, 14 May 2021 (UTC)
  • There's some sort of error in the citation "{{Harvard citations|nb=yes|year=2003|last1=Simons|loc=§4.2.1"
    Fixed. —Quondum 23:11, 7 May 2021 (UTC)
  • Some of these books refs it would be nice to have page numbers, if possible to help with verifiability
    I analyzed a few of these:
    • General references for broad topics that do not need page numbers: Curtis 2003 (footnote 21), Weyl 1952 (footnote 50), Bishop 1993 (footnote 52), Mumford et al (footnote 63), Fulton & Harris (footnote 66), Serre 1977 (footnote 67), Rudin 1990 (footnote 68), Artin 1998 (footnote 70), Ronan 2007 (footnote 77), Husain 1966 (footnote 79)
    • Has a page number, but in the full reference not the footnote and should probably be made more consistent: Bersuker 2006 (footnote 54)
    Done. Jakob.scholbach (talk) 09:56, 12 May 2021 (UTC)
    • Needs page numbers: Welsh 1989 (footnote 62), Kurzweil & Stellmacher 2004 (footnote 74)
    Done for Kurzweil. Welsh does not mention the Mathieu group, so this might better be replaced by some other reference. Jakob.scholbach (talk) 09:56, 12 May 2021 (UTC)
    • Can probably be replaced by a better reference: Lay (footnote 64), Kuipers (reference 65)
    • Not sure whether needs pages: Shatz 1972 (footnote 81)
    Is OK, I think. Jakob.scholbach (talk) 09:56, 12 May 2021 (UTC)
    —David Eppstein (talk) 21:50, 11 May 2021 (UTC)

Well, frankly, I understood little of this, so I may just be plain wrong on my comments. Hog Farm Talk 22:05, 7 May 2021 (UTC)

No worries, that's just alright. Jakob.scholbach (talk) 13:03, 8 May 2021 (UTC)
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