This question was recently deleted. The question had positive score, both answers had positive score, and one had been accepted. It had been closed as well (there's a separate question here about the point of closing questions that are "finished").

Anyway there had been no activity for a couple of days, and so with all of the above said: why would it be deleted? What is the point of deleting questions that have finished their entire lifecycle? I understand the motivation behind closing it (not enough context), even though I disagree with it (the question generated two different approaches to the problem, and I thought had a net positive value to the site). But really it's the deletion I cannot understand at all.

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    The way I view the situation for an abstract question is that the question should never have been "finished", and the deletion is meant to discourage people from finishing the question. – user1729 Sep 27 at 12:11
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    @user1729: Thanks for taking the time to explain the difference on meta (I'm glad someone did!). Isn't this throwing the baby out with the bathwater though? It's very possible to answer "homework" questions with hints, and then the site I believe nets a gain of mathematical content. But if one answer goes too far, we just scrap it all? Does this "pretty question" you mention exist on this site? Or were they all deleted? – Steve D Sep 27 at 12:19
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    The question was targeted in the CRUDE chatroom as a PSQ or Problem Statement Question. Evidently, many folks think that verbatim statements of homework are not appropriate for the site and the folks who frequent CRUDE attempt to enforce this collectively. Not everyone agrees. – Mark McClure Sep 27 at 12:24
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    @MarkMcClure: Wow, thanks! This is getting interesting...I'm guessing they don't require proof the question was a homework question, as long as it just "fit the mold"? I've long thought this site had a deletion problem, and it seems (IMO) to be worse than I thought. – Steve D Sep 27 at 12:28
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    @SteveD Correct, A PSQ is a PSQ it seems. I tend to agree with you that deletion has become too aggressive but I can understand that some folks don't want the site to be a homework mill. It's tricky issue that's been discussed quite a lot on Meta, for example here and here earlier this year. – Mark McClure Sep 27 at 12:32
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    @SteveD The question is a problem statement, the asker provides no context, shows no research, and includes no work/effort. By definition the question does not meet quality standards of this site. It reads as if it is a copy-and-pasted exercise from a text-book. You, as an answerer to a PSQ/problem-statement, will be at risk, like you were in this case, to losing points that are ill-gained from answering a very low quality question, when that question is closed and, if necessary, deleted. Invest your time and effort into answering questions that show effort and/or context. – amWhy Sep 27 at 16:49
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    @amWhy: thank you for the command. I would urge you to invest your time and effort into improving low-quality questions, rather than deleting them. I disagree entirely with your premise: deleting a question deletes the answers, and you seem to feel you cannot separate one from the other. I firmly believe that is false. – Steve D Sep 27 at 17:03
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    I gave you no command; I merely said that poor questions are at risk of being closed, and if very poor, they risk being deleted. That also deletes answers to the very low quality posts. I never told you what to do; just don't pretend you don't know what you're doing when you answer crap, SteveD. And, answering crap encourages those users who asked crap, to ask more crap, and others who see the crap, who think they can post homework or crap for "us to do for them", makes answerers of crap party to the ongoing influx of home-work style "do my work for me!" demands on this site. – amWhy Sep 27 at 17:07
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    If the question had finished its entire lifecycle, that seems to me like a reason in favor of deleting it. – Carl Mummert Sep 27 at 20:43
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    "Invest your time and effort into answering questions that show effort and/or context." "I never told you what to do" Sorry, @amWhy, I think you did tell SteveD what to do. – Gerry Myerson Sep 27 at 23:03
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    @amWhy, did the linked post tell everyone what to do, while at the same time saying it never told anyone what to do? – Gerry Myerson Sep 27 at 23:11
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    @amWhy, if I were refereeing a paper, and I perceived an inconsistency in the author's argument, and I pointed out the inconsistency in my review, I wouldn't consider it to be an attack on the author, and I hope the author wouldn't characterize it as an attack. I hope you and I can continue to have robust discussions, without either one of us feeling under attack. – Gerry Myerson Sep 28 at 1:29
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    @user1729: I do think it has that aspect, but unlike preventing people from answering these questions in the first place - which seems equally intractable - cleaning up afterwards appears to be more possible. – Carl Mummert Sep 28 at 14:34
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    @user1729 That's only because you've been spared from a site with far more crap than exists now, thanks to the hard work of folks who insist on maintaining as high quality of a site as possible. You just don't see, or look for, the mounds of trash that would have choked this site if it had not been closed and deleted. So indeed, this approach as worked from keeping this site from suffocating in crap, though to be sure, crap still enters, but also, we make sure crap leaves. You're welcome. – amWhy Sep 28 at 18:28
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    @amWhy Those so-called PSQs are the low-hanging fruit IMHO. Deleting a "bad" question from (usually) a new user is easy, even more so when coordinated between a few like-minded fellows who don't care if good answers go down the drain along. But lowly PSQs with no good answers tend to vanish on their own, anyway. They'll come at the bottom of searches, and will eventually be garbage-collected. Instead, I wish more of that effort went towards identifying/merging duplicates, which are at least as annoying, and a lot harder to deal with automatically. – dxiv Sep 29 at 4:01

Well, I can't see the deleted question but I can pretty much understand the situation after seeing your question and comments. This is not a proper answer but instead a very long comment in which I would just try to answer your quotes. This will be long but I am sure you won't mind :-)

The question had positive score, both answers had positive score, and one had been accepted

First of all, don't start beautifying/judging a question/answer with the number of upvotes/downvotes it has got. Read it and then decide for yourself. There are many rep-farmers and mystery users who up-vote low-quality questions/answers or may down-vote good questions/answers. Many times votes are cast due to personal choices and opinions. So using scores to start your question is not a good idea.

I understand the motivation behind closing it (not enough context)

So you understand that the question is a PSQ and from now I'll assume it is because I can't see the question, but it's quite clear from the comment section.

even though I disagree with it (the question generated two different approaches to the problem, and I thought had a net positive value to the site). But really it's the deletion I cannot understand at all

Now my question is why do you consider the question to be adding positive value to the site when you know that it's a PSQ? Is it because "it's a good problem that is interesting or hard to solve"? Well, that might be a good reason in general but not according to this site's policies. I think that you are quite an experienced user on this site and you already know quite a bit, but I'll mention it again. This site is for everyone one and for any level of mathematics. A good question or a quality question on this site is a question that shows user's motivation to learn through their research work, thoughts and in the best case scenarios, any type of attempts made to solve the question. If the user doesn't show their motivation for their question, it simply means that they are too lazy to work, or they don't want to learn, they just want others to do their homework, and this is not allowed in MSE or probably any SE.

But what's the discouragement? The asker got an answer to their question

The question wasn't meant to be answered at all. The moment you answer a PSQ you should be prepared to get down-voted and possibly deleted. If you can't accept this then I am afraid that you don't understand the policies of this site very well.

It's very possible to answer "homework" questions with hints, and then the site I believe nets a gain of mathematical content.

No, the site doesn't gain any good content irrespective of how good the question is: if the user is not motivated enough to show context. If you still don't understand look at the flagging statement of MSE below:

This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level.

I tend to agree with you that deletion has become too aggressive but I can understand that some folks don't want the site to be a homework mill.

IMO aggressiveness of deletion is actually proper now that is if you compare it with the history of MSE. Previously, there were fewer users and the policies were not enforced aggressively, which was not correct, but then those were the initial stages of the site and users learned and now they (most of them at least) are experienced enough to act according to the site's policies.

I left this site years ago because of how poorly it was managed. Things don't seem to have improved at all.

If by improvement you are referring to the reduction of aggressiveness towards the deletion of poor posts then you are very wrong, this site is not well suited for poor posts at all.

If I spend a lot of effort in producing a high-quality answer, and then another user -- with no context but enough rep -- comes along and deletes it

The answer is simple don't spend your time answering a PSQ, rather, as you have already asked from us, try to improve the PSQ by motivating the author and once the question has quality with the author's motivation, you may very well post your high-quality answer.

I think the answer went on too long but finally, I would like to say that the site's tough/unfair/harsh (if you consider it like that) policies are for a reason. I can give you a few:

  1. This is a professional site with countless students, scholars, teachers, professors, Master's candidate, Ph.D. candidates etc. When they are there to invest there precious time and share their knowledge with the asker, why can't the asker be motivated enough to solve their own question? Is that what you want this site to become? Ph.D. teachers solving home-works? You should notices that the services you are getting here for free, you won't find it anywhere even if you pay for it. Hence, please don't take the site for granted. Respect the policies that help maintain discipline and the professionalism. This respect is directly conveyed to everyone who is contributing here.
  2. If homework/low-quality/PS questions are allowed this site will be no different from countless other discussion forums, where no one bothers about anything and the askers think that they can use the site however they like for completing their homework like it's their birthright. If it happens, you will lose the dedicated people I have mentioned above in my first point.
  3. As I have mentioned before: The motivation to learn. The website is actually teaching you ways to improve your approach. A first timer doesn't know how this website works but if they are keen to solve their question and learn then they will stick around and take constructive criticism from the down-votes, comments, etc. and keep on improving the post.

This is how I learned and I have been here for just more than 2 months. You have been here for 3 years, I hope you understand better than me.

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    I thank you for your answer. Its content (and the quick upvotes it has gotten) show there is quite a large group of users on this site who somehow agree with what you're saying, no matter how condescending and off-the-mark it is. I don't think it worth my time going in on a line-by-line rebuttal here, but I will mention one thing: you don't need a Ph.D. to make your time valuable. – Steve D Sep 27 at 19:36
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    @SteveD I respect your opinion. Also, I didn't mean Ph.Ds. in a way you are referring. I just meant that if you want a quality answer, you need to have a "quality" question. My quote Ph.D. teachers solving home-works was just meant to increase the intensity of what I am trying to say and it applies to everyone who spent their valuable time here. I'll be happy to answer your questions(if you have any) with my opinions like I have done with this post here. – paulplusx Sep 27 at 19:45
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    In my opinion, what distinguishes this site is that it is for well written mathematical questions at all levels. It is not intended for hastily composed posts or for posting homework problems verbatim. We have a dedicated thread How to ask a good question, and "provide context" is one of the key aspects there. – Carl Mummert Sep 27 at 20:41
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    @SteveD Surely my linguistic abilities are not what they should be, but I fail to discern in this answer the condescension you see fit to mention in your comment. – Did Sep 27 at 20:48
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    @paulplusx There is this myth that all PSQ askers are vile cheaters who expect the answer on a plate just to pass it on, and therefore deserve to be punished, along with any fools who dared post answers. That's not always the reality, maybe not even most often the reality. I have seen many PSQ posters engaging in comments after posting, which showed that they had tried, but didn't grasp the "finer" point of having to include their failed attempts just in order to gain MSE sympathy. There are a handful of MSE users who still paint all PSQs the same color, and vote them down to death. – dxiv Sep 28 at 4:53
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    ...They also tend to be the more vocal ones on these meta topics, but don't confuse activism for legitimacy. I suggest you wait for more than 2 months and form your own opinion over time. As for the case in point here, @SteveD's wasn't even a complete answer. Had the OP of that question been one of those stereotypical lazy cheaters, SD's answer was useless since it could not be copy/pasted in their homework sheet, anyway. Yet, it got "thrown out with the bathwater", as SD's comment put it. – dxiv Sep 28 at 4:53
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    @dxiv $(1/4)$ Thank you for your advice. I never judge PSQ askers on their first impression(in this case their very question). I do encourage them to show what they have tried and if they know how to proceed I suggest them to show their thoughts (even if that's not correct), and by that, I mean just tell anything you think about the question. Additionally, I tell them to let us know the source of the question and also if the asker knows any related rules/formulae/concepts even remotely related to the subject of the question. – paulplusx Sep 28 at 5:16
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    $(2/4)$ This method only works if the asker is determined to solve the question even if they don't have(or they think they don't have) much knowledge about it. I call this leeching out work from a motivated user and I think most of the people I know here try to encourage the user a number of times before giving up using similar methods. It's true that I need to wait and observe a lot more but from what I have seen is that almost everyone tries their best to help motivate the asker but to that what I see is, the PSQ askers(most of them) are not bothered at all, – paulplusx Sep 28 at 5:17
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    $(3/4)$ they don't reply(i.e. they ignore) to the motivating comments and directly go to the answers/hints given to them by PSQ answerers. In these cases(and these happen frequently) not only the answerer is impeding the learning cycle of the asker but also the asker doesn't care at all and doesn't even pay any heed to the constructive criticism or the helpful comments. – paulplusx Sep 28 at 5:17
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    $(4/4)$ From what I have observed till now most of the thrown out with the bathwater questions have askers without any motivation and answerers with an overwhelmingly good heart to help(that they tend to forget/ignore MSE's context policy) or they are rep-farmers. Please don't misunderstand me, I am stating my image of MSE now. I can't see the original question for which this post is all about, so all I can do is make assumption seeing the OPs question on meta and his/her comments. I might be wrong making some assumption but I feel this is generally true for PSQ askers and answerers. – paulplusx Sep 28 at 5:22
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    @dxiv I believe that this sentence is a bit of a strawman: There is this myth that all PSQ askers are vile cheaters who expect the answer on a plate just to pass it on, and therefore deserve to be punished, along with any fools who dared post answers. Perhaps there are people who think this, but I would hazard to guess that the vast majority of vocal PSQ opponents really don't care if it is homework or not. Rather, such questions are simply ill-suited for this site. Whether or not the original asker is trying to cheat, MSE is not meant to be a solutions manual to standard math texts. – Xander Henderson Sep 28 at 23:28
  • @XanderHenderson I'll refer you to the last sentence in my other comment. – dxiv Sep 29 at 3:44

One of the stated goals of Stack Exchange is to create a repository of good, well-asked questions of general interest with correspondingly high quality answers. The goal is not to help individuals with specific problems at a specific moment in time (though if a specific user is helped, all the better), but to create a searchable database of question-answer pairs that are useful to a large number of people.

Part of what makes a question useful for people in the future is context. A copy-pasted question from a textbook is definitely useful for the person asking the question, and likely useful for anyone else who is using that particular textbook. Such a question might be useful for someone studying out of a similar book, and it might have broader appeal, but it seems to me that the general interest in such a question is minimal. As such, a bare-bones question which simply states a problem (which may or may not come from a textbook, and may ore may not be a homework problem) is not likely to be of general interest, and is therefore not appropriate for this site. The question you cite is such a question, hence it is reasonable that it has been closed and deleted.

It is possible that the original asker of that question could improve it. To do so, they would need to provide some context. Where did the problem come from? Why is the problem interesting? Why is it hard? What are the basic terms begin discussed? For that particular problem, it might be useful to know why the asker believes that $\ker(\varphi) = [G,G]$---without that information, an answerer might produce a proof that is essentially identical to a proof that the asker has already read but doesn't understand. Even a description of what the asker has attempted to do can provide a minimal level of context which will help answerers to provide useful answers which get to the heart of the problem.

Regarding upvotes on the question and answer: neither the question nor the answers actually have that many votes, and there are a couple of downvotes, too. My impression of the community's reaction that question is that is kind of "meh". It should also be pointed out that votes are only a proxy for quality, and that there are a lot of reasons that one might vote (either up or down) which have nothing to do with quality (for example, one might upvote a question which one has answered in order to enhance their own reputation; one might upvote a question because it was posted by a friend; or one might upvote a question because they are taking the same class with the same homework problem). If a question has a lot of upvotes or downvotes (say, more than 10 upvotes, or more than 3 downvotes---people downvote much less frequently than they upvote), then we might believe that the vote totals are a good proxy for quality, but two or three upvotes doesn't say very much.

Finally, regarding closure and deletion of questions with answers, I think that quid♦'s answer to another meta question sums things up nicely: we should judge questions on their own merits. If a question is closed and not improved, then it should be deleted. The existence of a good answer is not sufficient to justify keeping a bad question, though the existence of a great answer might be.

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    "The existence of a good answer is not sufficient to justify keeping a bad question, though the existence of a great answer might be." How about the existence of seven good answers? – Gerry Myerson Sep 27 at 23:04
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    @xander Nicely explained, especially the goals of the site. I think I was getting more personal with my opinions, you state it in a more general way, including more precise points. – paulplusx Sep 28 at 0:41
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    @GerryMyerson My first impulse is to say that the difference between a good answer and a great answer is qualitative: a great answer changes the way that you think about a question. A great answer is in some way inspired or unusually creative or insightful. It brings new wisdom to the site. No number of merely good answers can do that. Hence I do not think that any number of good answers is enough to justify keeping a bad question. Even for a great answer, my recommendation would be to close and lock the topic. – Xander Henderson Sep 28 at 1:11
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    If, somehow, a bad question managed to earn a large number of good questions, my recommendation would be (a) re-ask the question in a way that meets the site's standards, then (b) ask for a merge. – Xander Henderson Sep 28 at 1:12
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    @XanderHenderson One of the stated goals of Stack Exchange is to create a repository of good, well-asked questions of general interest with correspondingly high quality answers. The goal is not to help individuals ... Sorry, but this badly distorts what MSE itself says on the tour page is its manifesto: "Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields ... With your help, we're working together to build a library of detailed answers to every question about math". – dxiv Sep 28 at 4:16
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    ...So users who posted those now-deleted answers were in their way lending help to the site, not violating its policies. Discouraging and/or punishing good answers goes directly against MSE's stated manifesto. Your position on this is pretty obvious, and you are of course entitled to it, but please don't post your interpretation of it as a given to try make it sound like it's a consensus, or some sort of site policy. – dxiv Sep 28 at 4:17
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    I find the argument that "Context makes a problem more appealing for future users" to be odd, and the polar opposite of what I feel. If I am searching for the answer to a question then I quite frankly don't care about where the person found it and what they tried. All I care about the answer. So a PSQ is appropriate here. On the other hand, a post with lots of context would help me give better help to the asker. As I said, this is precisely the opposite of what you claim. – user1729 Sep 28 at 9:09
  • (To be clear: I think context is important, but rather that your reasoning for this is flawed.) – user1729 Sep 28 at 9:29
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    @dxiv, your quote from the tour page seems to me to support the quoted part of Xander's argument. As for the three words you emphasise, "your help" includes casting votes to delete as well as answering questions. – Peter Taylor Sep 28 at 11:15
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    @dxiv I have not posted my answer as though it were a consensus. I have posted an answer. The votes on meta are meant to determine what the consensus is. Right now, there are 7 people who have voted to assert that they agree with me, and 3 who have voted to assert that they disagree. – Xander Henderson Sep 28 at 11:53
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    @user1729 I did not say that context make a question more "appealing" to future users. I said it make the question more useful. Leaving aside the fact that MSE is not meant to be a homework mill, a citation of the book from which a question is derived can make the question more easily findable via search. An explanation of why a problem is difficult can help narrow the focus of answers, helping future users with a similar difficulty quickly filter out answers that aren't going to be useful to them. Inclusion of basic definitions can save some Googling. And so on. – Xander Henderson Sep 28 at 11:58
  • @XanderHenderson You started with One of the stated goals of Stack Exchange is to create a repository of good, well-asked questions of general interest with correspondingly high quality answers. The goal is not to help individuals with specific problems at a specific moment in time .... You did not prefix it with it is my opinion that ..., which makes it sound like an axiomatic truth. You never mentioned that the official MSE statement of purpose "to build a library of detailed answers to every question about math" is substantially different from your version. – dxiv Sep 29 at 3:40
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    @dxiv Need I preface the entire answer with "This is my opinion..."? I thought that was self-evident... – Xander Henderson Sep 29 at 3:51
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    @XanderHenderson It is not self-evident when you seem to be attributing something to MSE, which doesn't match (or even goes against) one of their official lines. – dxiv Sep 29 at 4:08

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