Timeline for Could $F_\infty \rtimes Z$ be isomorphic to $F_\infty$?
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 8, 2012 at 14:05 | vote | accept | Kevin Schreve | ||
| Sep 8, 2012 at 14:05 | vote | accept | Kevin Schreve | ||
| Sep 8, 2012 at 14:05 | |||||
| Sep 7, 2012 at 1:04 | comment | added | Todd Trimble | If you want to combine your accounts, you can go over to meta and make that request (near the top of the page there are 4 "sticky" threads -- you'll see the thread that's relevant here). As for the math, you can either edit this question, or you can start a new question (the former might be a better option; you can refer back to this question obviously). Without having thought about it much, I think a necessary condition is that $\phi$ be injective. Other people may have more to say. | |
| Sep 6, 2012 at 17:50 | comment | added | user26257 | Thanks very much for the help Todd! I actually asked my question as an unregistered user and then registered, so there are now two Kevin Schreve accounts... I say this because I wanted to accept your answer but couldn't...your answer leads to a new question- which isn't very clear unfortunately- given some non-trivial homomorphism $\phi:\mathbb{Z} \rightarrow$ Aut($F_\infty$), is there any way to detect whether $F_\infty \rtimes_\phi \mathbb{Z}$is free? | |
| Sep 6, 2012 at 16:07 | comment | added | Todd Trimble | Sure, no problem! Yeah, you need 50 points to leave comments (and I just added another 10 for you). (Also, you get a few more points when you accept an answer as satisfactorily addressing your question -- there's a place where you can click for that.) Finally, I had earlier left a comment which I later thought was wrong and deleted; hope you didn't mind too much. | |
| Sep 6, 2012 at 14:50 | comment | added | user26257 | This isn't an answer- but this was my first question posted so I can't comment yet? Anyway, thanks very much for your answer. | |
| Sep 6, 2012 at 6:12 | comment | added | Todd Trimble | Oh, you're absolutely right, Fernando. I just assumed $\aleph_0$, but... good point. | |
| Sep 6, 2012 at 5:39 | comment | added | Fernando Muro | Let me remark that this works for any infinite cardinal, despite the question does not make precise what infinite is taking to define $F_\infty$. | |
| Sep 6, 2012 at 5:29 | comment | added | Todd Trimble | Yes, that's true, Mariano. | |
| Sep 6, 2012 at 4:54 | comment | added | Mariano Suárez-Álvarez | Your «plenty of examples» are, in a way, all, no? | |
| Sep 6, 2012 at 4:25 | history | edited | Todd Trimble | CC BY-SA 3.0 |
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| Sep 6, 2012 at 3:14 | history | answered | Todd Trimble | CC BY-SA 3.0 |