Timeline for If each strict subgroup of G is free, must G be free or cyclic of prime order ?
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 3, 2012 at 21:07 | vote | accept | js21 | ||
| Oct 3, 2012 at 20:03 | comment | added | HJRW | It's a well known open question whether there's a non-free word-hyperbolic group with every proper subgroup free. | |
| Oct 3, 2012 at 16:49 | comment | added | Francesco Polizzi | Search on Google "almost free groups" | |
| Oct 3, 2012 at 16:48 | answer | added | Anton Klyachko | timeline score: 27 | |
| Oct 3, 2012 at 16:48 | comment | added | Misha | I think, strict=proper. Then there are even finitely-generated groups $G$ where every proper subgroup is infinite cyclic, but $G$ is not virtually free (Olshansky's central extensions of Tarsky monsters). However, if you add the condition that $G$ contains a free nonabelian subgroup, I do not think there are any know counter-examples. | |
| Oct 3, 2012 at 16:35 | comment | added | Autumn Kent | What's a strict subgroup? | |
| Oct 3, 2012 at 16:31 | history | asked | js21 | CC BY-SA 3.0 |