Talk:Free abelian group/GA1

GA Review
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Reviewer: Urve (talk · contribs) 04:31, 2 January 2022 (UTC)

Hello there. I will be taking a look at the article. In your comments, you said that someone with familiarity would be helpful - I took a few graduate classes on algebra, and from a broad look, the article seems appropriate for those who entering the subject one level below. I'll take a closer look and offer my comments below soon - and if you disagree with anything I say, feel free to say so. Urve (talk) 04:31, 2 January 2022 (UTC)

I've been watching some of the work on the article for a few days, so I'm glad you nominated it for GA status. My comments below, which you are free to disagree with. As long as I can understand your thought process, I think it's all good.
 * The last few days were just a little more polishing before I finalized the nomination; most of my edits to this article were much earlier (beginning in 2013 after a couple smaller edits earlier). —David Eppstein (talk) 06:44, 3 January 2022 (UTC)


 * Just to be clear, I don't think the uncited paragraphs in "Definition and examples" problematic: They are common knowledge for who we are writing to. That may be a problem for DYK, though.
 * This may be too technical an article to be a good candidate for DYK in any case, so I wasn't planning on nominating it and am not too concerned about their stronger sourcing requirements, as long as the sourcing is good enough for GA standards. I added some sources for the definition of free abelian groups; however the definition of abelian groups themselves is still unsourced. —David Eppstein (talk) 05:52, 3 January 2022 (UTC)
 * This is just a thought, and not a suggestion that I've thought through very deeply. It may be useful for "in the corresponding polynomial, or vice versa" to demonstrate how isomorphisms are generally verified. Because we can do both of these mappings, it is isomorphic - but the general point is not really that there is just one map, right? Maybe "in the corresponding polynomial, and vice versa" would be helpful for illustration.
 * Ok, I added an example here, and a not-very-technical explanation of why this mapping is an isomorphism. —David Eppstein (talk) 06:06, 3 January 2022 (UTC)
 * "More generally the direct product of any finite number of free abelian groups is free abelian" - it might (I'm unsure) be useful to give a link to mathematical induction here, to give an idea for how the result is reached... perhaps something like "More generally, the direct product of any finite number of free abelian groups can be shown to be free abelian through mathematical induction"
 * Is induction really necessary? Just take the disjoint union of the bases. Why do you need to do it one step at a time? —David Eppstein (talk) 21:04, 2 January 2022 (UTC)
 * "it is a quotient of the free abelian group over" - we link quotient in the lead but not here - do you think that would be helpful? It is linked in the "Rank" section, but "overlinking" in the body can be useful when terms are not yet fully understood by the reader
 * Ok, re-linked. —David Eppstein (talk) 06:34, 3 January 2022 (UTC)
 * "Again, this is a group invariant" - this seems somewhat informal. Leaving it at "This is a group invariant" is probably enough - it's important enough to say again, but whether we need to stress its importance is not clear ... to me (your opinion welcome)
 * Ok, reworded. —David Eppstein (talk) 21:04, 2 January 2022 (UTC)
 * A minor point, but MOS:SAID has some useful instruction about the word claimed, as in "Solomon Lefschetz and Irving Kaplansky have claimed that ...". My immediate reaction was what the MOS guidance says - that their statements are not reasonable or based in evidence. I think we can easily say "have said" here, unless Kaplansky gives a reason to doubt it. (I don't have access to Kaplansky to check, so I leave it to you.)
 * Changed from "claimed" to "argue". The point of the wording was that this is really a statement of opinion rather than mathematical fact. —David Eppstein (talk) 21:04, 2 January 2022 (UTC)
 * What do you mean by "that solves the problem"?
 * I meant that meets the conditions stated earlier in the same paragraph, but I tightened the wording to remove this. —David Eppstein (talk) 21:04, 2 January 2022 (UTC)
 * "no group element (non-identity)" - I think it would be clearer if it were "no (non-identity) group element", but this may be an intentional choice.
 * I agree; reordered. I don't think the parens are necessary. —David Eppstein (talk) 05:31, 3 January 2022 (UTC)
 * Something feels off to me about "beyond having zero sum of multiplicities", but I'm not sure what it is. Maybe a zero sum? Or can we say something like "beyond having its multiplicities add to zero"?
 * Rewrote to use a simple conjunction ("must have multiplicities summing to zero, and meet certain additional constraints") rather than trying to compare the two kinds of constraints using "beyond". —David Eppstein (talk) 06:28, 3 January 2022 (UTC)

For the formalities,
 * Well-written: Yes, with some suggestions above
 * Verifiable: Yes, with why I don't find the uncited text problematic above; reliable sources; no original research that I can see; no copyvio (Earwig's picks up nothing worrying)
 * Broad: Yes
 * Neutral: Yes
 * Stable: Yes - there is some talk page discussion about how best to present the material, but there's not ongoing substantial changes or disputes
 * On images: They are good; illustrative; the rationales for use are clear; captions are useful. Regarding the image File:Lattice in R2.svg - I like where this is. You may also consider moving it down in the section to be closer to the information relating to lattices.
 * The lead is well-written and gives a good overview for the subject.

As an aside, I find the citations to specific exercises amusing. Not because they're a problem, but because this is perhaps the only field we can do that sort of thing :) Hungerford was what we used for some classes, solid book.

I'll leave it here, and if I think of anything more, I'll add some comments. I think it's clearly at GA level, but I hope my feedback can improve the article, or if I'm off with my comments, I hope I can understand better your choices. Urve (talk) 05:34, 2 January 2022 (UTC)
 * Thanks for the review! I'll try addressing your comments individually over the next few days as I find time. —David Eppstein (talk) 07:51, 2 January 2022 (UTC)
 * Ok, I think I've responded to everything; please take another look. —David Eppstein (talk) 06:34, 3 January 2022 (UTC)
 * Thanks so much. Re the induction thing: I just thought it would be a nice pointer - students will probably come across the article and wonder how that's done, but I'm sure they're able to recognize it, and it's not important to include. It's been a while since I taught algebra, but that was the approached we used - but no big deal. Just a thought.
 * I'll promote this shortly. Congratulations. Urve (talk) 07:07, 3 January 2022 (UTC)