Timeline for Cool problems to impress students with group theory [closed]
Current License: CC BY-SA 2.5
42 events
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| Nov 25, 2019 at 18:00 | review | Reopen votes | |||
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| Apr 29, 2019 at 16:40 | review | Reopen votes | |||
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| Sep 10, 2013 at 13:01 | review | Reopen votes | |||
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| Apr 14, 2013 at 1:47 | history | closed |
Benjamin Steinberg Fernando Muro Asaf Karagila♦ Ryan Budney Felipe Voloch |
no longer relevant | |
| Apr 13, 2013 at 1:16 | answer | added | Venkataramana | timeline score: 4 | |
| Jan 29, 2011 at 2:55 | answer | added | Tommaso Centeleghe | timeline score: 1 | |
| Jan 29, 2011 at 2:04 | answer | added | Mark Wildon | timeline score: 4 | |
| Jan 28, 2011 at 19:45 | answer | added | Greg Marks | timeline score: 2 | |
| Jan 28, 2011 at 18:33 | answer | added | Nick S | timeline score: 20 | |
| Jan 28, 2011 at 17:21 | answer | added | Allen White | timeline score: 4 | |
| Nov 16, 2010 at 4:59 | comment | added | Amritanshu Prasad | You ought to at least mention Galois' work on solutions of equations by radicals, since it was the first (and most spectacular) application of abstract group theory. Giving a proof in class would require a greater commitment than you seem to allow for. It solves two very old problems in geometry- trisection of angles, and construction of regular polygons by straightedge and compass. | |
| Oct 6, 2010 at 19:09 | answer | added | Ori Gurel-Gurevich | timeline score: 10 | |
| Oct 6, 2010 at 12:53 | answer | added | Simon Lyons | timeline score: 91 | |
| Oct 6, 2010 at 11:34 | answer | added | Colin Reid | timeline score: 9 | |
| Oct 6, 2010 at 8:59 | history | edited | Bjørn Kjos-Hanssen |
added arXiv tag
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| May 24, 2010 at 3:39 | answer | added | Brad Rodgers | timeline score: 25 | |
| Feb 12, 2010 at 0:46 | answer | added | Anonymous | timeline score: 10 | |
| Feb 4, 2010 at 17:37 | answer | added | Victor Miller | timeline score: 17 | |
| Feb 1, 2010 at 14:02 | answer | added | Pavel Etingof | timeline score: 32 | |
| Jan 30, 2010 at 2:03 | answer | added | Dan Piponi | timeline score: 12 | |
| Jan 30, 2010 at 1:54 | answer | added | Dan Piponi | timeline score: 62 | |
| Jan 30, 2010 at 1:27 | answer | added | Richard Stanley | timeline score: 8 | |
| Jan 29, 2010 at 23:04 | answer | added | Dinesh | timeline score: 8 | |
| Jan 29, 2010 at 19:17 | answer | added | Joseph Malkevitch | timeline score: 5 | |
| Jan 29, 2010 at 9:36 | answer | added | Andrea Mori | timeline score: 5 | |
| Jan 29, 2010 at 5:08 | answer | added | jeremy | timeline score: 3 | |
| Jan 29, 2010 at 4:50 | answer | added | Ben Weiss | timeline score: 12 | |
| Jan 29, 2010 at 3:59 | answer | added | KConrad | timeline score: 58 | |
| Jan 29, 2010 at 3:30 | comment | added | fedja |
Yes, but more often than not you can find elements in some finite group with the given set of relations and a non-trivial boundary word as well. I talked to my students a bit about presenting groups by generators and relations but so far the only way for us to show that so defined group is non-trivial/non-commutative/whatever was to produce an explicit non-trivial homomorphism to some familiar group (usually $\mathbb Z$, $\mathbb Z_n$ or $S_n$) or a family of such homomorphisms.
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| Jan 29, 2010 at 3:19 | comment | added | Qiaochu Yuan | The point is one can take quotients and hope that they are 1) finite, and 2) still prove that tiling is impossible. The example I know is dominos of size 1x2 and 2x1, where a certain quotient of the tiling group is S_3. | |
| Jan 29, 2010 at 3:17 | answer | added | Cam McLeman | timeline score: 3 | |
| Jan 29, 2010 at 3:13 | answer | added | Darsh Ranjan | timeline score: 41 | |
| Jan 29, 2010 at 3:10 | comment | added | Douglas Zare | Aren't the tiling groups usually infinite? jstor.org/pss/2324578 | |
| Jan 29, 2010 at 3:10 | answer | added | Mariano Suárez-Álvarez | timeline score: 4 | |
| Jan 29, 2010 at 3:07 | answer | added | user1504 | timeline score: 9 | |
| Jan 29, 2010 at 3:05 | answer | added | Mark Meckes | timeline score: 30 | |
| Jan 29, 2010 at 3:00 | comment | added | Qiaochu Yuan | The tiling problem is a great example; I can't help but think there's more to it than meets the eye, but I don't know anywhere that it's written down and developed in detail. Do you have a good reference? | |
| Jan 29, 2010 at 2:57 | answer | added | Qiaochu Yuan | timeline score: 55 | |
| Jan 29, 2010 at 2:46 | comment | added | fedja | Certainly. But not in the statement of the problem itself. | |
| Jan 29, 2010 at 2:41 | comment | added | Harry Gindi | Are group actions allowed? | |
| Jan 29, 2010 at 2:08 | history | asked | fedja | CC BY-SA 2.5 |