Timeline for Locally finite groups containing all finite groups
Current License: CC BY-SA 4.0
3 events
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| Sep 20, 2023 at 15:25 | comment | added | YCor | This is nice. A remark: for a group $G$, the existence of a finite subset whose centralizer is reduced to $Z(G)$ can be interpreted as: the closure $\mathrm{Inn}(G)$ is discrete (in $\mathrm{Aut}(G)$, endowed with the Onofri topology of pointwise convergence). For $G$ countable, $\mathrm{Aut}(G)$ is a Polish group. It is an open question whether there exists $G$ infinite countable locally finite such that $\mathrm{Aut}(G)$ is countable. A necessary condition for this is indeed that $\overline{\mathrm{Inn}(G)}$ is discrete, which is already a strong condition. | |
| Jun 30, 2023 at 21:38 | history | edited | Luc Guyot | CC BY-SA 4.0 |
Fixes a typo
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| Jun 30, 2023 at 16:35 | history | answered | Dave Benson | CC BY-SA 4.0 |