Timeline for "Big" groups $G$ with trivial $Out(G)$
Current License: CC BY-SA 3.0
7 events
| when toggle format | what | by | license | comment | |
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| Apr 7, 2017 at 12:54 | comment | added | ADL | It is worth pointing out that Bumagin-Wise (Every group is the outer automorphism group of a finitely generated group, J. Pure App. Alg. 2007) used a variation on Rips construction to prove that given any finitely presented group $Q$ there exists a finitely generated, residually finite group $Q$ such that $\operatorname{Out}(G_Q)\cong Q$. Here, $G_Q$ is the kernel of Rips construction, so if we take $Q$ to be trivial then $G_Q$ is $C{\prime}(1/6)$ and we get an explicit presentation. If $Q$ is finite then $G_Q$ is still hyperbolic, large, virtually compact special, etc. | |
| Mar 21, 2017 at 21:50 | history | edited | HJRW | CC BY-SA 3.0 |
Corrected attribution.
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| Mar 21, 2017 at 21:50 | comment | added | HJRW | @Seirios, you're quite right. It's usually called Paulin's theorem, although it's true that the version of the Rips machine that the argument uses was worked out by Bestvina and Feighn. | |
| Mar 20, 2017 at 20:06 | comment | added | Seirios | I think the result you mention about outer automorphism groups of hyperbolic groups should be attributed to Bestvina and Feighn: it is proved in their paper untitled Stable actions of groups on real trees (in fact, the first step of the proof is based on a construction due to Paulin). | |
| Mar 19, 2017 at 21:29 | comment | added | HJRW | @YiftachBarnea, yes, I mean large in the sense of Pride. | |
| Mar 19, 2017 at 21:22 | comment | added | Yiftach Barnea | Henry, just to make sure do you mean large in the sense that a subgroup of finite index maps on a non-abelian free group? | |
| Mar 19, 2017 at 21:14 | history | answered | HJRW | CC BY-SA 3.0 |