The OP disappeared, so I do not know who needs these answers. But I will do it now.

Good grief!

This is why the correct action would have been to keep the original question closed and to edit the new question so that it stood on its own. If a question makes you go "Hmmm", then the correct response if the original questioner has disappeared is to ask a new question. But make it a genuinely new question, not a repost. If a question gets embroiled and it's clear that people disagree about how to interpret the question then that is in itself a strong indication that the question is a bad question. If one of those interpretations is a good question, then ask that as a new question, clear of the ambiguity and controversy of the original one.

Mark, I do not consider myself "highly sensitive" - but who does consider themselves that? - , and I'm not "non-tenured" anyway so that remark clearly doesn't apply to me. I have no intention of listening to your words so cannot tell if they are nice or nasty. But based on your remarks here, I shall steer clear of you on MO in future.

@Anton: good. I will remove my question then - in two days according to the rule. Or you can delete it right now.

Sure, I'll delete it now.

@Todd: I agree that the last question is worth cutting out. I'd also remove the "Hello" and "Thank you" (though I wouldn't edit a question for the sole purpose of removing greetings). Would you mind doing this?

I also agree that it makes sense to trim down the comment thread, cutting out the bits that are no longer relevant. It would be best if everybody simply removed their own comments. For posterity, here's the current comment thread. I've linked to it from the question, so you should now feel free to delete your own comments without fear of confusing anybody.

You may reduce to a fixed prime number, since every abelian torsion group canonically splits into its primary parts. – Martin Brandenburg yesterday

If Z/3 * Z/9 * Z/4 * Z/8 is too complicated, why don't you try to understand Z/2 * Z/2? BTW, this is not the right medium for questions like that. – Franz Lemmermeyer yesterday

You may want to look at Goursat's Lemma, which determines the subgroups of a direct product group. Then specialise this to the abelian case. – José Figueroa-O'Farrill yesterday

Math Overflow is for mathematics researchers, whereas this is a standard coursework problem about the structure of finite abelian groups. As Franz said, this is not the right site to seek answers to such questions. Sorry. Try Math Stack Exchange perhaps. – Todd Trimble yesterday

This paper: Ganjuškin, A. G. Enumeration of subgroups of a finite abelian group (theory). Computations in algebra and combinatorial analysis, pp. 148–164, Akad. Nauk Ukrain. SSR, Inst. Kibernet., Kiev, 1978 gives an algorithm for enumerating all subgroups of a finite Abelian group. – Mark Sapir yesterday

On the other hand, the elementary theory of pairs (A,H) where A is a finite Abelian group and H is its subgroup is undecidable (see Taĭclin, M. A. Elementary theories of lattices of subgroups, Algebra i Logika 9 1970 473–483 and references there). Hence there cannot be a nice description of subgroups of finite Abelian groups (say, one cannot represent a pair (A,H) as a direct product of pairs of sizes bounded in terms of the period of A). – Mark Sapir yesterday

Voted to reopen. – Mark Sapir yesterday

This is a better reference than Taiclin. Slobodskoĭ, A. M.; Fridman, È. I.: Theories of abelian groups with predicates that distinguish subgroups. Algebra i Logika 14 (1975), no. 5, 572–575. – Mark Sapir yesterday

I wrote the Magma code for this - it does it roughly by enumerating matrices in Hermite Normal Form whose row span contains the list of invariants of the finite abelian group. – Derek Holt yesterday

This is actually an interesting question, and leads to interesting combinatorics. The problem of enumerating subgroups of a finite abelian group is both non-trivial and interesting. As far as I know, the reference "Subgroup lattices and symmetric functions" by Lynne M. Butler (Memoirs of the AMS, no. 539; MR1223236) reflects the state of art. It is beautifully written and has a good survey of the history of the problem. I vote to reopen this question. – Amritanshu Prasad 16 hours ago

@Derek and Amritanshu: I was trying to reopen this question, otherwise it will disappear in a day or two: meta.mathoverflow.net/discussion/773/… . But this is hopeless: the local "Moral Police" (Spanish Inquisition) does not like the question. My guess is that they hate finite Abelian groups (they certainly prefer cicadas). But it is just a guess. <b>Disclaimer.</b> I have nothing against the Moral Police or the Spanish Inquisition. – Mark Sapir 10 hours ago

I do not believe that Mark "trying to turn the question into something it is not". As asked, without any edits, this, in my opinion, is a perfectly legitimate question. To answer a request for classification by pointing out an enumeration is also very reasonable. I am grateful to Mark for bringing to my attention references that I was not aware of (why are all these great papers in Russian still so obscure?) – Amritanshu Prasad 7 hours ago

@Todd: you dont seem to have read the question carefully. It is not about the structure of finite abelian groups. It is about the classification of subgroups. – Amritanshu Prasad 7 hours ago

I have reposted the question and comments here: mathoverflow.net/questions/46244/… . – Mark Sapir 5 hours ago

As one of the original votes to close, here's my two penn'orth. I think the original question was pretty bad, but as Mark has shown, that very question does turn out to have an interesting answer. (I was going to say that I'm surprised that such a seemingly naive question has such an interesting answer, but of course we all know that lots of naive questions have interesting answers.) I don't think my original vote to close was a total mistake, but nevertheless I'm willing to admit that I may have been a little hasty. As such, I'm happy to cast the third (and final?) vote to reopen.

@Mark: I assume it's unintentional, but you're dehumanizing the people you're trying to communicate with. Yes, there are rules and procedures dictating how MO functions, but it is ultimately run by people, and I have every reason to believe those people are reasonable. It's like you've gone to a friend's home for dinner, noticed that it's possible for her to stab you with her knife, and thereafter assume that she's just looking for the opportunity to do so. I'm imagining conversation along the lines of "No, I won't pass you the salt, you asshole." If you continue to use MO (or the rest of the internet), you will ultimately have to get over the fact that other people have control over content you put on MO (e.g. can edit it). But that's okay! Other people also have control over the supply line that terminates in the food in your refrigerator.

Let's step back from all the knives for a moment and come back to the original question.

The PO presented a number of obvious subgroups of a finite Abelian group, and asked if these are all. My answer showed that (a) an enumeration of all subgroups is possible (there is an algorithm) and (b) no nice description is possible, in particular the description in the question is not complete. The answer not only shows that this description is not complete, but that in a sense there are no nice descriptions at all.

I actually completely agree with this. Though Mark's answer is more sophisticated than the question, it really is an answer to the question as it was asked. The asker may not be able to appreciate the machinery involved, but the phrasing of the question indicates to me that he/she would appreciated the core message, "no, those aren't all the subgroups."

The question isn't well-written: it's two and a half questions slapped together. But I can imagine myself having those questions (and, in light of Mark's answer, I would certainly fail to answer them), so I'd like to think the content is fine for MO.

The opposition to reopening the original question seems unshaken, but I feel like that might be an artifact of the heated discussion. I want to get my opinion in, but I don't want to act unilaterally, so I commit two reopen votes for the original question. That is, if it gets up to three reopen votes, I'll reopen it.

While (as I mentioned once above, before you snapped unpleasantly in my direction) I have no opinion whatsoever on the mathematics of the question under discussion (not being well versed in that particular subject), I do have an opinion on keeping MathOverflow as "positive" as possible. In particular, I disagree with your characterisation that those "other" parts of the question is "insignificant". To me, setting a civil tone of voice is significant to the well-being of MathOverflow, and hence my vote.

Your comment about "ganging up" is what I suspected going on here, and I found it quite ugly.

That is actually quite insulting.

My intentions were entirely honourable. If I were part of a "cartel" out to get you (do I really have that much spare time?), would I have tried to explain my action here? Why would I have even bothered to try to improve your question? I (and the others in my "gang") would simply have flagged it as spam. Problem solved, and you'd have no idea who was "ganging up" on you.

As for "taking liberty". I did not "take a liberty" in the sense of doing something that is technically possible but isn't meant to be done. In submitting your question, you accepted the fact that some people could edit it in order to try to improve it. I'm one of those people. If you don't like that, you shouldn't submit a question here.

I'm not going to get in to an edit war. I encourage you to reconsider the rollback and rather think about:

How can I best get an answer to the question that I'm really interested in?

What I tried to do was separate the mathematical question (which belongs on MO) from the surrounding fluff (which belongs, if anywhere, here). As it stands, the question would turn off anyone who tried to actually engage with the mathematics because of all the surrounding discussion. In my experience such questions do not get answered as those who would be interested are wary of entering the fray.

At the moment, I'd consider closing as "subjective and argumentative" since it clearly is promoting an argument!

In general, I would like to suggest that all the people arguing insignificant parts of my question concentrate on the question itself.

So I've removed all the insignificant parts so that people can concentrate on the question itself and not bother with the argument over the original question (which was quite rightly closed).

Mark, your fears about deletion are completely groundless. If you won't accept our word for it ("our" = +10k users) then I wonder that you repost the question since we might just gang up on you, close, and delete this question as well! Ultimately, we all rely on our opinions of Anton, since he's in ultimate control of this place. I've never met him, so all I have to go on is the behaviour that I've observed. So far, he's seemed an extremely decent and reasonable person. So I'm sure that if an honest question got deleted and there was a good reason for keeping it visible, he'd listen to reason and undelete it.

Note that even deleted questions are never truly gone. Users with 10K rep can see deleted questions and answers so if it does get deleted, you can always ask someone to find it and copy it for you. Or you can get it out of the public database that Anton makes available. Or you could take a snapshot now, host it on your own site, and put a (discrete!) link to it from the current question.

To comment on the wider point, here are some things that I've learnt whilst using MO (and, in MO terms, I'm an old-timer). Firstly, great answers do not make great questions. If the original questioner wouldn't understand your answer then it is a waste of time and effort posting it. Secondly, if a question makes you think of a new question, then post that new question! It is okay to ask-and-answer your own question - so long as you're honest about it. If you do it too much, people will vote against you, so it's self-limiting, but it can be a very good way of correcting common misconceptions. But asking-and-answering and asking-a-related-question are two different things. In this case, it seemed to be the latter, not the former.

yesterday VERY IMPORTANT ! ! [closed]

yesterday Hi there ,I am stuck here in trying to prove the theorem [closed]

2 days ago Riemann goes away [closed]

2 days ago Riemann goes over

2 days ago Discrete Probability

Nov 13 at 12:37 Riemann goes over [closed]

Nov 13 at 9:32 Who can explain this zeta [closed]

Nov 11 at 16:40 Is there any abstract definition of value?

Nov 10 at 16:52 Conformal mapping of C \ D* onto C \ (-1, 1)

Nov 9 at 8:51 Denested version of sqrt(5+sqrt(5)). [closed]

Nov 9 at 8:49 Equation of ln(-1). [closed]

Nov 9 at 7:23 a doubt on birch and swinnerton dyer conjecture [closed]

Nov 8 at 1:12 Edward Frenkel and PhD [closed]

Nov 6 at 6:14 Opportunity Cost and Time [closed]

Nov 6 at 6:10 Graduate School Differences [closed]

Nov 6 at 5:54 precomact set in L2 space

Nov 4 at 4:18 What is so special about this matrix? [closed]

Nov 1 at 23:46 helping for money [closed]

Oct 28 at 17:22 rank mathematicians from best to worst [closed]

Oct 28 at 16:38 Dishonest article [closed]

Oct 28 at 2:53 What is the easiest way to find the maximum of 9cos(t) - 8cost(3t)? [closed]

Oct 27 at 11:43 Status of OPN Conjecture — NEARLY RESOLVED [closed]

Oct 22 at 11:47 Since there is more than one notion of nothing, why is there only one zero axiom? Is an alternati… [closed]

Oct 22 at 11:43 The large component of the fuck graph

Oct 18 at 6:05 Discrete Structures and Complexity

It is pretty much all obvious homework requests and spam. The ones that look like they have reasonable titles were either homework requests or incoherent. If you are not sure about some of these I could also post their text.

Mark, can you just ask your question and remove all the rest, leaving the relevant references and explanation? A good 80 percent of the text of the original question you copied is unrelated to your question, and I don't see the point of copied over the comments: Derek's, for example, has nothing to do with what you are asking.

If you're really keen, leave a comment on the old closed question pointing to your new better one, too.

When life gives you lemons, make lemonade. When life gives you limes, make margaritas!

Would it be acceptable for markvs to ask the question he wants to answer, and then answer his own question?

I'm in favor of people asking new questions when there's a question which admits an interesting reading which is almost certainly not what the asker was after. Here are a couple of examples:

• This question was closed, but Kevin Buzzard asked this question as a result.
• This question was closed, but I asked this question as a result.

Of course, there's no harm in acknowledging the bad question as the inspiration for the interesting question.

If you already know the answer to a question, but you think the question (and answer) are really cool and you want people to know about it, I don't see what's wrong with asking the question and then answering it. I would hold off on the answer for at least a day because an answer posted by the asker tends to kill enthusiasm for the question. What would be even better is if you could include the answer in the background of a related question for which you don't know the answer.

I can give examples of several recent questions which were not closed and where the OPs clearly did not know what they wanted.

is no justification for not closing a question, as have been discussed here before. MO should not be allowed to sink to the lowest level of pointless questions just because all the 3K+ users decide to take a night off and head to the pub. The point of the voting for closure/re-opening is (for MO) to keep the level high, rather than maintaining an arbitrary lowest common denominator.

When a question is being discussed for possible closure or reopening, only the merits of the question should be involved. (Note this is similar to how in real life, you can't get out of a speeding ticket just because everyone else is doing it but not being caught.)