Timeline for Embedding f.g. groups in 2-generated groups
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27 at 18:24 | comment | added | Ian Agol | @MoisheKohan The 237 Coxeter grou is 2-generated (see theorem A) link.springer.com/content/pdf/10.1023/A:1005032526329.pdf | |
| Jul 27 at 15:47 | comment | added | YCor | (From the abelianization, the 246 reflection group is not generated by less than 3 elements; if it's maximal, we're done.) | |
| Jul 27 at 15:42 | comment | added | YCor | @MoisheKohan How do you prove that the 237 reflection group is not 2-generated? | |
| Jul 27 at 14:49 | comment | added | Lee Mosher | Ah, shoot, I mis-thought this. I thought about the triangle groups but not the van Dyck groups. | |
| Jul 27 at 14:47 | comment | added | Moishe Kohan | @MattZaremsky: Yes, fundamental groups of all compact orientable surfaces embed as finite index subgroups in 2-generated groups. | |
| Jul 27 at 14:46 | comment | added | Moishe Kohan | But if you take, say, the reflection group $(2,3,7)$, it will be maximal NEC group and, hence, cannot embed in a 2-generated group. | |
| Jul 27 at 14:46 | comment | added | Matt Zaremsky | I think $\pi_1(S_2)$ admits a finite-order automorphism that's transitive on a generating set (right?), which seems like a recipe for embedding with finite index in a 2-generated group. | |
| Jul 27 at 14:36 | comment | added | Moishe Kohan | No, plenty are 2-generated (van Dyck groups). | |
| Jul 27 at 14:27 | history | answered | Lee Mosher | CC BY-SA 4.0 |