Timeline for Classification of finite subgroups of $\mathrm{SL}_5(\mathbb{C})$
Current License: CC BY-SA 4.0
13 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 26, 2021 at 17:53 | comment | added | Richard Lyons | @AbdelmalekAbdesselam: If I'm reading correctly, Blichfeldt did not miss any collineation groups, i.e., subgroups of $PSL_3(C)$. | |
| Jul 25, 2021 at 19:30 | comment | added | Richard Lyons | @AbdelmalekAbdesselam:Thanks for pointing this out. | |
| Jul 25, 2021 at 16:55 | comment | added | Abdelmalek Abdesselam | @RichardLyons: yes. It seems that even Blichfeldt missed some subgroups too, as per Yau and Yu in "Gorenstein Quotient Singularities in Dimension Three" bookstore.ams.org/memo-105-505 That's quite a tricky problem. | |
| Jul 24, 2021 at 15:45 | comment | added | Geoff Robinson | There is a helpful list of low dimensional finite complex linear groups in the article by W.Feit in the Proceedings of the 1970 ICM, held in Nice. | |
| Jul 24, 2021 at 15:43 | comment | added | Geoff Robinson | Since you did not restrict to irreducible groups, you also need the list of irreducible finite subgroups of ${\rm GL}(4, \mathbb{C})$ in addition to the groups given in Richard's answer. These groups were also know to Blichfeldt (at least the primitive ones). There were some omissions/errors, eg one found by Conway. | |
| Jul 23, 2021 at 23:34 | comment | added | Richard Lyons | @AbdelmalekAbdesselam: Blichfeldt credits Jordan but points out that Jordan missed two perfect subgroups of $SL_3(C)$, namely $GL_3(2)$ and $3A_6$, of orders $168$ and $1080$. | |
| Jul 23, 2021 at 18:15 | comment | added | Abdelmalek Abdesselam | I think the original result for SL3 is due to Camille Jordan digizeitschriften.de/dms/img/?PID=GDZPPN00215675X | |
| Jul 23, 2021 at 16:02 | comment | added | Richard Lyons | @TheoJohnson-Freyd: See H.F. Blichfeldt, The finite, discontinuous, primitive groups of collineations in three variables. Math. Ann. 63 (1907), no. 4, 552–572. | |
| Jul 23, 2021 at 15:22 | answer | added | Richard Lyons | timeline score: 13 | |
| Jul 23, 2021 at 14:59 | comment | added | Theo Johnson-Freyd | Incidentally, what is the classification for SL3? I only know the SL2 case. | |
| Jul 23, 2021 at 14:07 | history | edited | YCor | CC BY-SA 4.0 |
formatting
|
| Jul 23, 2021 at 14:06 | review | First posts | |||
| Jul 23, 2021 at 15:07 | |||||
| Jul 23, 2021 at 14:04 | history | asked | Luc | CC BY-SA 4.0 |