Timeline for Copies of $\mathbb{Z}\oplus \mathbb{F}_2$ in non-affine, irreducible Coxeter groups
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 27, 2020 at 9:40 | vote | accept | worldreporter | ||
| Mar 6, 2020 at 14:01 | history | edited | Magma | CC BY-SA 4.0 |
added 4 characters in body
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| Mar 6, 2020 at 13:55 | comment | added | Magma | Ah, that's nice. | |
| Mar 6, 2020 at 13:48 | comment | added | YCor | If $C$ is a 1-ended f.g. group, every free inversion-free action on a tree fixes a vertex. Apply this to the action of $A\ast B$ on its Bass-Serre tree: $C$ fixes a vertex, and the vertex stabilizers are the conjugates of $A$ and $B$ precisely. | |
| Mar 6, 2020 at 13:46 | comment | added | Magma | @YCor How does one see this directly? | |
| Mar 6, 2020 at 13:39 | comment | added | YCor | One directly sees that if a free product $A\ast B$ contains a 1-ended group $C$, then $C$ is conjugate to a subgroup of $A$ or $B$. This applies to $C=F_2\times Z$, or more generally to any direct product of two infinite f.g. groups. | |
| Mar 6, 2020 at 13:30 | history | answered | Magma | CC BY-SA 4.0 |