Timeline for Centralizers of elements in HNN extensions
Current License: CC BY-SA 3.0
4 events
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| Apr 13, 2017 at 12:58 | history | edited | CommunityBot |
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| Mar 6, 2014 at 13:52 | comment | added | bemihai | Thank you very much for the comment. Actually, I realized that this is implicitly contained in the paper of Karrass and Solitar, namely if $H$ and $\theta(H)$ are malnormal in $G$ and $H^g\cap \theta(H)=1$, for all $g$, then the centralizer of a nontrivial element is as above. But is not clear what happens with the centralizer if a conjugate of $H$ touches $\theta(H)$. | |
| Mar 4, 2014 at 12:44 | comment | added | Ashot Minasyan | One needs to be careful here. E.g., if $\theta:H \to H$ is the identity, then the $\Gamma$-centralizer of any $h \in H$ is the direct product $C_G(h) \times \langle t \rangle$. Also, if $\theta$ maps any $h \in H$ into $ghg^{-1}$ for some $g \in H$, then the centralizer of $t^{-1}g$ will not be cyclic either. The natural sufficient requirement for the desired property should be that $H^g \cap \theta(H)=\{1\}$ for all $g \in G$. | |
| Mar 4, 2014 at 10:46 | history | asked | bemihai | CC BY-SA 3.0 |