Timeline for Normal subgroups of automorphism group of infinite cubic tree
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jan 20, 2018 at 3:08 | comment | added | YCor | To conclude, the famous notion of groups acting on a tree without inversion is not a natural notion. Essentially, it has only been coined so as to ensure that if there's a bounded orbit then there's a fixed vertex. The natural notion is the notion of bipartite-preserving action, i.e. an action through the group of index $\le 2$ of automorphisms preserving some bi-coloring. | |
| Jan 19, 2018 at 22:55 | comment | added | YCor | Sorry, your edit is also not correct. Indeed, consider a loxodromic element $f$ in $G-G^+$. Let $H$ be a maximal subgroup among those subgroups containing $f$ and without element acting with edge inversion. Then $H$ is not what you want. | |
| Jan 19, 2018 at 22:46 | history | edited | Misha | CC BY-SA 3.0 |
added 297 characters in body
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| Jan 16, 2018 at 1:23 | comment | added | YCor | The first given definition of $G_+$ is not correct. One correct definition of $G_+$ is that it is the subgroup of those $g$ such that for all $x$ we have $d(x,gx)\in 2\mathbf{Z}$. One other is that it is the set of $g$ preserving a 2-coloring (a map from vertices to $\{0,1\}$ such that adjacent vertices have different colors) - of course there are 2 2-colorings, not just 1, and this is why this subgroup has index 2. The coset $G-G^+$ contains loxodromic elements, which have no inversion. | |
| Feb 25, 2014 at 9:10 | vote | accept | Dominik | ||
| Feb 24, 2014 at 22:07 | comment | added | Misha | @Dominik: Yes, it is equivalent, just the matter of taste. | |
| Feb 24, 2014 at 20:58 | comment | added | Dominik | Thanks for the answer. But wouldn't it be easier to say that, given the unique 2-coloring of $T$, $G_+$ consists simply of the color-preserving automorphisms of $T$? | |
| Feb 21, 2014 at 23:20 | comment | added | Ian Agol | One could also have a look at Serre's book "trees": springer.com/mathematics/algebra/book/978-3-540-44237-0 | |
| Feb 21, 2014 at 20:45 | history | answered | Misha | CC BY-SA 3.0 |