Timeline for What did Frobenius prove about $M_{12}$?
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
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| May 11, 2019 at 14:21 | comment | added | Sam | The article has since been accepted and can be found ahead of print here: dx.doi.org/10.22108/ijgt.2019.115366.1531 | |
| Jun 26, 2018 at 9:09 | history | edited | Nick Gill | CC BY-SA 4.0 |
Added a reference to recent preprint on the topic.
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| Mar 1, 2018 at 13:52 | comment | added | Frieder Ladisch | I think there was no doubt about $M_{12}$ already in 1904 (maybe on $M_{24}$): E.g., in the 1st edition from 1897 of his book, §109, Burnside describes a "tentative process" by Jordan to determine whether any given $k$-transitive group of degree $n$ is contained in a $(k+1)$-transitive group of degree $n+1$. In a note to §108 at the end of Chapter VIII, he proves Jordan's theorem on sharply transitive groups, and sketches how to get generators of $M_{12}$ by this process. In §153, he gives again generators of $M_{12}$, and an exercise to derive various properties of this group. | |
| Feb 28, 2018 at 21:15 | vote | accept | Nick Gill | ||
| Feb 28, 2018 at 15:00 | answer | added | Frieder Ladisch | timeline score: 17 | |
| Feb 28, 2018 at 14:04 | answer | added | Geoff Robinson | timeline score: 8 | |
| Feb 28, 2018 at 13:48 | history | edited | Nick Gill | CC BY-SA 3.0 |
added a question that hones in on what I'm looking for.
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| Feb 27, 2018 at 10:19 | comment | added | Nick Gill | @jwsiegel, Let me reiterate, also, that although Mathieu did discover these groups and all the assertions he made about them were correct, there was considerable doubt in the mathematical community as to whether or not these groups were distinct from the alternating groups -- and this doubt was not resolved until Witt came along in the 1930's. If even the order of these groups was not "properly known", it's hard to imagine what other properties Frobenius might have made use of... | |
| Feb 27, 2018 at 10:18 | comment | added | Nick Gill | @jwsiegel, that's interesting. I wonder, though, what properties of the Mathieu groups he was using. Mathieu "wrote his groups down" by giving permutations that generated them... I wonder if Frobenius made use of the specific given permutations in any way? | |
| Feb 27, 2018 at 3:18 | comment | added | jwsiegel | Based on the first paragraph of section 5 in the paper, he claims that the only 5-transitive groups on at most 24 elements other than the symmetric and alternating groups are two groups discovered my Mathieu. He then proceeds to calculate their character tables. It sounds like Mathieu had already shown their existence from what Frobenius says in his paper. | |
| Feb 26, 2018 at 11:04 | answer | added | Carlo Beenakker | timeline score: 16 | |
| Feb 26, 2018 at 10:48 | history | asked | Nick Gill | CC BY-SA 3.0 |