Timeline for Quadratic extension of quadratic extension
Current License: CC BY-SA 3.0
19 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 29, 2011 at 23:37 | vote | accept | Wanderer | ||
| Oct 29, 2011 at 23:23 | comment | added | Gerhard Paseman | Wanderer, I am hoping that you will show gratitude to Greg for answering your question, preferably in a comment to his answer, and perhaps also by accepting his answer. For the benefit of readers to come, I hope we all will provide more context and light, and not much more presumption and heat. Gerhard "Really, Really Likes Motivating Remarks" Paseman, 2011.10.29 | |
| Oct 29, 2011 at 23:12 | comment | added | Wanderer | @Mark, Franz and others: I'm very happy with the point Gil makes. I am sure you are sometimes stuck on a "trivial" question yourself (just admit it :)). There is no such thing as a trivial triviality... | |
| Oct 29, 2011 at 21:31 | comment | added | user6976 | @Greg: This question is formulated as a homework. It can easily be a homework question in the first graduate algebra course. The question is about subgroups of $S_4$. All subgroups of $S_4$ are described in any graduate algebra course. So the question should be trivial for anybody, not just for number theorists. Of course not all trivial questions should be closed. But the ones that are formulated like homeworks (without any motivation, etc.) should be closed. | |
| Oct 29, 2011 at 21:11 | comment | added | Gil Kalai | It is a very common experience, not only for junior researchers but also for experienced one, that some questions that you are stucked with in your research turn out to be easy, even trivial, when you see the answer. Not being shy or embarassed to ask is very important. People, doing research in mathematics, should not be shy or embarassed to ask on MO. There was a legitimate concern that this was a homework question that followed by a detailed explanation by the OP that it wasn't. This should have been the end of the (non-mathematical) discussion. | |
| Oct 29, 2011 at 19:42 | comment | added | Greg Kuperberg | @Franz I understand that if you work in number theory or finite group theory, then the question can be regarded as trivial. Or even that it should be called trivial. But I think it was Grothendieck's view that the best kind of mathematics is a sum of interesting trivialities. (I also understand that the result in question is really due to Galois, not Waterhouse, but still.) | |
| Oct 29, 2011 at 19:17 | comment | added | Franz Lemmermeyer | @Wanderer and Greg: The question is completely trivial, and Waterhouse would not in a lifetime dream of writing an article about this question. I gave Waterhouse's article because it answers a much more general question in a very nice way. I most certainly do not think that a question that has been answered in the literature is off topic here. | |
| Oct 29, 2011 at 16:29 | comment | added | Gil Kalai | I agree with Greg, and, for what it worth, I vote not to close. | |
| Oct 29, 2011 at 15:56 | comment | added | Greg Kuperberg | Guys, could you just give the question the benefit of the doubt. It could be given as graduate-level homework, but so could a lot of things. And citing a paper from only 20 years ago as an answer --- that's a good way to answer questions in MO, and not a good way to argue that they should be closed. | |
| Oct 29, 2011 at 14:14 | comment | added | Todd Trimble | Wanderer: I'd think that people are less blithe about voting down than voting up, since a point is deducted from one's own reputation for each downvote. As for voting to close: yes, people sometimes jump to conclusions too quickly, for example if the question is in terms that high school students can understand (but actually turns out to be tricky). My own guess is that most people would give pause before entering a vote to close than they would a vote up. Either way, one shouldn't get too excited by upvotes, or too upset by votes to close. (Easier said than done!) | |
| Oct 29, 2011 at 14:04 | comment | added | user9072 | @Wanderer: I think one 'problem' with your question was really the superficial fact that it was phrased in a typical homework/excercise style. It is true that the context you later gave does not add much to the question itself. Yet, from observing a lot of question, I can asure you that it can make a considerable difference whether some personal motivation is given or not. In some sense one can consider this as strange, but in my experience it is like this. | |
| Oct 29, 2011 at 13:24 | comment | added | Wanderer | Yes, I know that the upvotes might come from people who have barely read the question. Isn't the same thing true for the votes to close? Sometimes people just like voting down - for no particular reason... | |
| Oct 29, 2011 at 13:02 | comment | added | Todd Trimble | Wanderer, you are probably taking upvotes way too seriously here. The fact is, no one knows who is doing the upvoting; it might include people who haven't thought the question through. You might also be taking closing votes too seriously/personally. | |
| Oct 29, 2011 at 12:35 | comment | added | Wanderer | Thanks for the link. About the question itself: the question was voted up five times. I can find the answer in a research article. Hence I can only conclude that this is an OK question for Mathoverflow... | |
| Oct 29, 2011 at 12:06 | comment | added | Franz Lemmermeyer | This question is not appropriate for MO. You can find your questions answered in Waterhouse's beautiful article "The normal closures of certain Kummer extensions", Can. Math. Bull. 37, No.1, 133-139 (1994). | |
| Oct 29, 2011 at 0:49 | answer | added | Greg Kuperberg | timeline score: 10 | |
| Oct 29, 2011 at 0:45 | comment | added | Tom Goodwillie | Hints: (1) The Galois group of the splitting field of a degree four extension is a subgroup of $S_4$. (2) Think of a group having a subgroup of index $2$ that in turn has a subgroup of index $2$. | |
| Oct 28, 2011 at 22:37 | comment | added | Gerhard Paseman | It may not be homework, but it still looks like it. If you want the question to be more suitable, you might mention what you have tried or what specific difficulty you have in answering the question. I am hoping that you are familiar with the MathOverflow FAQ and its contents by now. Gerhard "Also Finds Galois Theory Challenging" Paseman, 2011.10.28 | |
| Oct 28, 2011 at 21:46 | history | asked | Wanderer | CC BY-SA 3.0 |