Timeline for Embedding $\mathrm{SL}_n(3)$ into $\mathrm{SL}_n(p)$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Feb 29 at 17:25 | comment | added | YCor | That $|\mathrm{SL}_n(3)|$ divides $|\mathrm{SL}_n(p)|$ is rare but still true in many cases. It seems automatic for $n=2$, and for each $n$ seems true for infinitely many $p$ (I haven't checked, but it might be true inside one coprime arithmetic progression). It's more and more rare as $n$ grows. For instance for $n=7$ the smallest such $p$ is $535573$. | |
| S Feb 29 at 3:04 | vote | accept | user44312 | ||
| S Feb 29 at 3:04 | vote | accept | user44312 | ||
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| S Feb 29 at 3:04 | vote | accept | user44312 | ||
| S Feb 29 at 3:04 | |||||
| Feb 29 at 3:04 | vote | accept | user44312 | ||
| S Feb 29 at 3:04 | |||||
| Feb 29 at 3:04 | vote | accept | user44312 | ||
| Feb 29 at 3:04 | |||||
| Feb 28 at 14:24 | answer | added | Geoff Robinson | timeline score: 11 | |
| Feb 28 at 13:43 | answer | added | Dave Benson | timeline score: 11 | |
| Feb 28 at 12:47 | comment | added | user44312 | Yes, I agree. It is already rare that $|\mathrm{SL}_n(3)|$ divides $|\mathrm{SL}_n(p)|$. | |
| Feb 28 at 12:30 | comment | added | Geoff Robinson | I would agree with that assessment. | |
| Feb 28 at 12:29 | history | edited | YCor | CC BY-SA 4.0 |
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| Feb 28 at 12:28 | comment | added | Dave Benson | And I'll bet the answer is never, for $n>2$ and $p\ne 3$. | |
| Feb 28 at 12:26 | comment | added | Geoff Robinson | I think this can be attacked by considering the Sylow $3$-subgroups of the respective groups. | |
| Feb 28 at 12:17 | history | asked | user44312 | CC BY-SA 4.0 |