Timeline for Heuristic argument that finite simple groups _ought_ to be "classifiable"?
Current License: CC BY-SA 4.0
21 events
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| Sep 12, 2022 at 17:00 | history | edited | Glorfindel | CC BY-SA 4.0 |
broken link fixed, cf. https://meta.mathoverflow.net/q/5301/70594
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
replaced http://mathoverflow.net/ with https://mathoverflow.net/
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| Apr 13, 2017 at 12:19 | history | edited | CommunityBot |
replaced http://math.stackexchange.com/ with https://math.stackexchange.com/
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| Dec 8, 2016 at 22:39 | history | edited | GH from MO |
edited tags
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| Jun 12, 2012 at 15:01 | comment | added | Gerald Edgar | Why should it be easier to classify simple groups than to classify primes? (Which is, after all, the Abelian case of "classify the simple groups".) | |
| Sep 27, 2010 at 23:18 | comment | added | Peter Shor | I don't think any of the answers so far give a good reason classification should be possible. I doubt whether there's a good way to tell whether classification is possible in general. For example, to ask a question motivated by quantum computation that I've occasionally wondered about: can you classify polynomial time algorithms that compute periodic functions where the period is exponential in length? How would you answer this question? | |
| Sep 27, 2010 at 21:08 | answer | added | JGis | timeline score: 10 | |
| Sep 17, 2010 at 16:49 | answer | added | John Goodrick | timeline score: 17 | |
| Sep 13, 2010 at 16:45 | vote | accept | Tim Campion | ||
| Sep 12, 2010 at 8:31 | comment | added | Laurent Moret-Bailly | @Mariano: "Sporadic: Occurring at irregular intervals or only in a few places; scattered or isolated" (Oxford American Dictionary). I don't see why this should imply finiteness. | |
| Sep 11, 2010 at 12:25 | answer | added | Pietro | timeline score: 4 | |
| Sep 9, 2010 at 22:11 | answer | added | Terry Tao | timeline score: 25 | |
| Sep 9, 2010 at 14:28 | comment | added | j.p. | If one really understood, why there are no (non-cyclic) finite simple groups of odd order, maybe then one had enough insight about finite simple groups and could hope for a good answer to your question. (To my knowledge, the proof of the odd-order theorem goes by obtaining enough information about a minimal counterexample until one finally is able to construct it by calculating its presentation, when it evaporates due to a contradiction.) | |
| Sep 9, 2010 at 14:27 | history | edited | Tim Campion | CC BY-SA 2.5 |
second guessing...
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| Sep 9, 2010 at 14:26 | comment | added | Mariano Suárez-Álvarez | @Joseph, if there were infinitely many sporadic groups they would not be sporadic :) | |
| Sep 9, 2010 at 13:50 | answer | added | Richard Borcherds | timeline score: 70 | |
| Sep 9, 2010 at 12:27 | comment | added | Andrew Stacey | The word "heuristic" refers to a particular method of finding a solution to a problem. Could you clarify exactly what you mean by it as that doesn't seem to fit with the question? My reading of your question is that you mean: "Is there an accessible explanation of why the finite groups are classifiable?". | |
| Sep 9, 2010 at 12:04 | comment | added | Peter Shor | I would say that one of the things that makes groups possible to classify is that they have an enormous amount of structure attached (e.g., representation theory, etc.). On the other hand, there are also classes of objects with very little structure that are also possible to classify; it's the ones with an intermediate amount of structure that seem to be difficult. | |
| Sep 9, 2010 at 11:45 | comment | added | Joseph O'Rourke | I asked a related question on Math StackExchange: "Why are there only a finite number of sporadic groups?" math.stackexchange.com/questions/2427/… | |
| Sep 9, 2010 at 10:48 | comment | added | Sheikraisinrollbank | An (easier?) question that one should be able to answer first: why should finite dimensional simple Lie algebras (over the complex numbers) be "classifiable"? Whatever heuristic works for groups ought to be applicable there too. | |
| Sep 9, 2010 at 10:05 | history | asked | Tim Campion | CC BY-SA 2.5 |