Timeline for The largest primes in the monster group construction
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4 events
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| Apr 4, 2018 at 12:03 | comment | added | Tito Piezas III | @S.Carnahan: There is also the coincidence $163+67+43+19+11+7 = 310$ where $310$ is the number of objects involving certain moonshine groups. Kindly see this post. | |
| Mar 31, 2018 at 11:37 | comment | added | Tito Piezas III | If you look at all $194$ degrees of the irreducible representations of $\mathbb{M}$ as A001379 sequence $1, 196883, 21296876, 842609326, \dots$, then $$\begin{aligned} 196883 &= 47\times 59\times 71\\ 21296876 &= 2^2\times 31\times 41\times 59\times 71\\ 842609326 &= 2\times 13^2\times 29\times 31\times 47\times 59 \end{aligned}$$ and so on, with precisely the same prime factors also dividing the order of $\mathbb{M}$. | |
| Jul 17, 2016 at 7:02 | comment | added | S. Carnahan♦ | The first rule of moonshine is that there are no coincidences. That said, if you look at the dimensions of smallest nontrivial representations of other sporadic groups, you also get the largest prime factor or two in the order. For example, $4371 = 3*31*47$, and the largest prime factors in the order of the baby monster are 31 and 47. Anyway, the fact that the dimension of an irreducible representation must divide the order of the group should cut down on the surprise a bit. | |
| Jul 16, 2016 at 14:45 | history | asked | ClassicalPhysicist | CC BY-SA 3.0 |