Timeline for Groups surjecting onto a free group
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 9, 2011 at 15:41 | comment | added | Igor Rivin | Cool, will be watching for it! | |
| Nov 9, 2011 at 15:17 | comment | added | Ashot Minasyan | @Igor, this has not appeared yet, but we will hopefully post in on arXiv within the next few days. | |
| Nov 9, 2011 at 15:05 | comment | added | Igor Rivin | @Ashot: thanks! I have seen a fair bit on RAAG, but missed this result! | |
| Nov 9, 2011 at 14:25 | comment | added | Ashot Minasyan | Igor, one positive result is that any non-abelian subgroup of a right angled Artin group (also called a graph group) surjects onto $\mathbb{F}_2$. It is a current research theme in Geometric Group Theory to show that many groups embed into right angled Artin groups (at least virtually). Thus the class of such ``very large'' groups is indeed quite extensive. | |
| Nov 7, 2011 at 15:58 | vote | accept | Igor Rivin | ||
| Nov 7, 2011 at 12:00 | comment | added | Matthias Künzer | Since free groups are projective, I'd say: G semidirect F(X), where F(X) is the free group on a set X, where G is an arbitrary group and where the action of F(X) on G is given by an arbitrary map X -> Aut(G). But maybe I misunderstood the question? | |
| Nov 7, 2011 at 10:29 | comment | added | Martin Brandenburg | Since every non-abelian free group surjects to $F_2$, an equivalent question is: What are the extensions of $F_2$? I don't see a connection to HW's large groups yet. | |
| Nov 7, 2011 at 10:17 | answer | added | HJRW | timeline score: 13 | |
| Nov 7, 2011 at 10:02 | history | asked | Igor Rivin | CC BY-SA 3.0 |