Timeline for Examples of totally disconnected, locally compact non-sigma-compact groups
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
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| Mar 30, 2011 at 21:07 | comment | added | Yiftach Barnea | BTW, the paper should soon appear in TAMS. So we have just fixed quite a lot of typos that are still in the current version. | |
| Mar 30, 2011 at 20:57 | history | edited | Yiftach Barnea | CC BY-SA 2.5 |
added 1370 characters in body
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| Mar 30, 2011 at 17:48 | comment | added | Colin Reid | Take a profinite group $G$ with $VZ(G)=1$ such that $Out(G)$ is uncountable. Then $Comm(G)_S$ is not $\sigma$-compact because the embedded copy of $Aut(G)$ is not $\sigma$-compact (topologically it's a disconnected union of uncountably many copies of $G$). Conversely if $L$ is a non-$\sigma$-compact t.d.l.c. group with a countably based open compact subgroup $U$, then some open subgroup of $U$ must have non-$\sigma$-compact normaliser, because there are only countably many pairs of open subgroups of $U$. | |
| Mar 30, 2011 at 11:39 | comment | added | Tom De Medts | @Yiftach: Could you elaborate on how you would show that some of the classes of groups occuring in your paper are not $\sigma$-compact? | |
| Mar 30, 2011 at 11:19 | comment | added | Abel Stolz | This looks interesting. Thank you for the hint. | |
| Mar 30, 2011 at 10:57 | history | answered | Yiftach Barnea | CC BY-SA 2.5 |