Timeline for Finitely generated subgroups with infinite cyclic quotient
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 25, 2018 at 11:56 | answer | added | AGenevois | timeline score: 5 | |
| Jul 27, 2010 at 22:38 | comment | added | HJRW | Apologies, Victor. I was addressing your remark "This construction was generalized by Bieri". | |
| Jul 27, 2010 at 21:19 | comment | added | Victor Protsak | I know, Henry, that's precisely why I put the quote marks around it. | |
| Jul 27, 2010 at 20:19 | vote | accept | Mustafa Gokhan Benli | ||
| Jul 27, 2010 at 20:01 | comment | added | HJRW | Victor, a very slight historical nitpick: the example studied by Stallings is one level up, namely the corresponding subgroup of $F_2\times F_2\times F_2$ (which gives an example of a fp group with infinitely generated $H_3$); Bieri then generalised this construction for an direct product of any number of free groups. Presumably this subgroup of $F_2\times F_2$ was known before Stallings's paper. | |
| Jul 27, 2010 at 19:44 | comment | added | Victor Protsak | No. F.p. groups $G$ with a f.g. but not f.p. subgroup are known as "incoherent". "Bieri-Stallings example": $G=F_2\times F_2$ and $H$ is the kernel of the map to $\mathbb{Z}$ sending each of the 2+2 free generators of the factors to 1. This construction was generalized by Bieri and further by Bestvina-Brady to higher finiteness properties. | |
| Jul 27, 2010 at 17:02 | answer | added | HJRW | timeline score: 15 | |
| Jul 27, 2010 at 16:13 | history | asked | Mustafa Gokhan Benli | CC BY-SA 2.5 |