Timeline for If G is a finitely generated group with vcd(G) finite, is vcd(H) finite for H, where H is an automorphism group of G?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Feb 26, 2023 at 21:11 | vote | accept | Mike | ||
| Feb 26, 2023 at 20:04 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Feb 26, 2023 at 17:13 | history | edited | Moishe Kohan | CC BY-SA 4.0 |
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| Feb 26, 2023 at 17:12 | comment | added | Moishe Kohan | Oh, this should be corrected. I only claim injectivity which suffices. | |
| Feb 26, 2023 at 17:11 | comment | added | Matt Zaremsky | I see why the map $G\to Aut(N)$ induces an injective map $Q\to Out(N)$, but is it really always surjective? In any case, injectivity is enough to ensure $Out(N)$ has infinite vcd once $Q$ does, as desired (and maybe $Q$ really is isomorphic to $Out(N)$ and I'm just being dense). | |
| Feb 26, 2023 at 16:25 | comment | added | Moishe Kohan | @Mike: no nontrivial element of $G$ commutes with all elements of $N$ (by hyperbolicity). | |
| Feb 26, 2023 at 16:23 | comment | added | Mike | Thanks. How do you get to Out(N)≅Q, though? | |
| Feb 26, 2023 at 15:38 | history | answered | Moishe Kohan | CC BY-SA 4.0 |