Timeline for What finite simple groups we can obtain using octonions?
Current License: CC BY-SA 4.0
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| Jan 2, 2019 at 12:15 | answer | added | user21230 | timeline score: 1 | |
| Jan 2, 2019 at 11:59 | history | edited | user21230 | CC BY-SA 4.0 |
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| Jan 2, 2019 at 11:50 | comment | added | Todd Trimble | @MarekMitros Hi, yes, despite the jokes above, I meant Community Wiki. If you look under the answer box on the right, you'll see the button. | |
| Jan 1, 2019 at 18:50 | review | Close votes | |||
| Jan 5, 2019 at 11:34 | |||||
| Jan 1, 2019 at 16:51 | comment | added | Sylvain JULIEN | @Todd : you mean no CW complex is needed ? : -) | |
| Jan 1, 2019 at 16:45 | history | edited | LSpice | CC BY-SA 4.0 |
Minor proofreading; names of papers; PDF -> abs
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| Jan 1, 2019 at 14:43 | comment | added | Todd Trimble | Hi Marek. The incorporation of discoveries, additions, etc. into the question begins to make the question hard to read, or even to locate in the text. An alternative might be to collect the information you have subsequently obtained in an answer below the question. You can make the answer CW if you like. | |
| Jan 1, 2019 at 12:51 | history | edited | user21230 | CC BY-SA 4.0 |
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| Jan 1, 2019 at 12:44 | history | edited | user21230 | CC BY-SA 4.0 |
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| Jan 1, 2019 at 12:39 | history | edited | user21230 | CC BY-SA 4.0 |
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| Aug 28, 2017 at 11:53 | comment | added | user21230 | Robert Wilson defined Leech lattice using octonions. In this definition point $[1,0,0]$ correspond to E8 sublattice $[\lambda, 0,0 ]$, point $[\bar s,\bar sj,0]$ correspond to $[\lambda\bar s, \lambda\bar sj,0]$ and e.g. $[s,1,1]$ correspond to $\lambda s,\lambda,\lambda]$. Vector $\lambda$ belong to some $E_8$ lattice in octonions. Octonion vector can be treated as point on projective octonion plane. See maths.qmul.ac.uk/~raw/pubs_files/octoLeech1rev.pdf | |
| Aug 28, 2017 at 11:01 | comment | added | მამუკა ჯიბლაძე | What do you mean by "result of 819 points"? | |
| Aug 28, 2017 at 6:26 | history | edited | user21230 | CC BY-SA 3.0 |
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| Jul 31, 2017 at 8:03 | comment | added | David Roberts♦ | @DerekHolt since that is a popular mathematics book, I'm not sure it will have the kind of details you mention earlier in your comment! I guess this is something by Buekenhout along those lines: The geometry of the finite simple groups | |
| Jul 31, 2017 at 6:58 | history | edited | user21230 | CC BY-SA 3.0 |
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| Jun 9, 2017 at 7:04 | comment | added | user21230 | I am reading "Symmetry and the Monster" again and I must to delete my previous comment. The book is quite interesting. But hearing about 255-pages proof of Feit and Thompson makes me think that it is hopeless to achieve something in group theory... | |
| Jun 2, 2017 at 10:01 | comment | added | Derek Holt | I am afraid I have not been keeping up-to-date with this topic. There was an attempt by Buekenhout and many of his students to describe them all using Buekenhout geometries, but that is 30-40 years old and has probably obscolescent. I have an idea that there might have been more recent alternative attempts but I don't remember any details. For the Monster, you could try the book "Symmetry and the Monster: The Story of One of the Greatest Quests of Mathematics " by Mark Ronan. | |
| Jun 2, 2017 at 9:44 | comment | added | user21230 | @Derek: Can you show example of such work ? Especially for groups from monster family and pariahs. I am interested in construction of the group as automorphisms of some object, for example lattice or algebra. | |
| Jun 2, 2017 at 9:09 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 20:29 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 11:44 | comment | added | Derek Holt | I think the problem of finding a uniform description of the sporadic groups is interesting and important, and a number of people have worked on it, but unfortunately nobody has come up yet with a satisfactory answer, and it is possible that there isn't one! | |
| May 31, 2017 at 11:40 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 10:40 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 10:23 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 9:41 | comment | added | user21230 | Thank you all for keeping my (possibly poor) question here... | |
| May 31, 2017 at 9:28 | comment | added | Stefan Kohl♦ | @Derek: Sure you cannot literally 'vote' against closing -- but I think your comment actually counts more than a vote! | |
| May 31, 2017 at 9:20 | history | reopened |
Derek Holt Myshkin Henry.L Friedrich Knop Stefan Kohl♦ |
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| May 31, 2017 at 8:55 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 8:44 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 8:26 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 8:20 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 7:59 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 31, 2017 at 6:04 | comment | added | user21230 | Thank you for this comment, prof. Holt. It is really consolation for me. | |
| May 30, 2017 at 22:01 | review | Reopen votes | |||
| May 31, 2017 at 9:20 | |||||
| May 30, 2017 at 21:45 | comment | added | Derek Holt | I am afraid it has been closed, but I voted to reopen. It's a pity that it's not possible to vote against closing. | |
| May 30, 2017 at 19:32 | history | closed |
Stefan Kohl♦ R.P. Lee Mosher Tom De Medts Andy Putman |
Needs details or clarity | |
| May 30, 2017 at 10:17 | comment | added | user21230 | My question is about to be closed. I have question to administrators. Why this question was not closed: mathoverflow.net/questions/136880/…. It is also about definition of finite groups and it is hard to answer - either positive or negative way. | |
| May 30, 2017 at 10:14 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 30, 2017 at 6:41 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 29, 2017 at 12:41 | history | edited | Myshkin | CC BY-SA 3.0 |
+ top level tag (gr.)
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| S May 29, 2017 at 12:00 | history | suggested | Martin Sleziak | CC BY-SA 3.0 |
corrected several typos and added link - the same as in the previous post by the same OP: https://mathoverflow.net/questions/264832/24-vectors-in-leech-lattice-having-scalar-product-frac14-pairwise
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| May 29, 2017 at 11:55 | review | Suggested edits | |||
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| May 29, 2017 at 6:54 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 28, 2017 at 12:45 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 27, 2017 at 8:49 | comment | added | user21230 | @Schlieper What are your doubts regarding imaginary octonions ? I tested this definition in GAP for q=2,3,4 and it works. I must check the details and I can quote my scripts if you are interested. | |
| May 26, 2017 at 20:37 | comment | added | W. Cadegan-Schlieper | Oops, I meant to say finite field octonions in the first comment | |
| May 26, 2017 at 20:32 | comment | added | W. Cadegan-Schlieper | That said, the real octonions and integral lattices inside can be used to define the Leech lattice, whose symmetry group is a sporadic finite simple group. | |
| May 26, 2017 at 20:31 | comment | added | W. Cadegan-Schlieper | I don't think you've actually defined imaginary octonions... | |
| May 26, 2017 at 19:27 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 26, 2017 at 19:25 | review | Close votes | |||
| May 26, 2017 at 23:53 | |||||
| May 26, 2017 at 19:19 | comment | added | user21230 | I added definitions in the question. | |
| May 26, 2017 at 19:19 | history | edited | user21230 | CC BY-SA 3.0 |
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| May 26, 2017 at 19:04 | comment | added | Stefan Kohl♦ | What precisely do you denote by $L_x$ and $R_y$, and what do you mean by imaginary perpendicular octonions? | |
| May 26, 2017 at 18:49 | history | asked | user21230 | CC BY-SA 3.0 |