Timeline for Does the group given by this presentation have an element of order 2?
Current License: CC BY-SA 3.0
5 events
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| Apr 16, 2011 at 16:26 | comment | added | JeremyKun | No. It is definitely an HNN extension of a free group. I just posed the more general question because I didn't know of this theorem on HNN extensions, and thought to answer it from a different angle. | |
| Apr 16, 2011 at 4:19 | comment | added | Autumn Kent | Note that my answer only works when $G$ is in fact an HNN-extension of a free group, which isn't obviously the case for all groups with the kind of presentation you've given. (For instance, the relations could be $t^{-1}x_i t = x_1$ for all $i$, and so $t$ isn't giving you an isomorphism between subgroups.) Could that be the source of the problem? | |
| Apr 16, 2011 at 3:31 | comment | added | JeremyKun | This is unfortunate for at least one author who I'll leave anonymous, because it provides a counterexample to a theorem in one of his books on one relator groups. | |
| Apr 15, 2011 at 4:23 | vote | accept | JeremyKun | ||
| Apr 14, 2011 at 22:36 | history | answered | Autumn Kent | CC BY-SA 3.0 |