Timeline for Is a "central" extension of $\mathbb{Z}/m\mathbb{Z}$ by $\mathrm{GL}_n$ necessarily split?
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 1, 2014 at 15:40 | vote | accept | Kestutis Cesnavicius | ||
| Nov 1, 2014 at 14:10 | answer | added | anon | timeline score: 6 | |
| Nov 1, 2014 at 5:52 | answer | added | Derek Holt | timeline score: 9 | |
| Nov 1, 2014 at 5:17 | comment | added | Kestutis Cesnavicius | Could you elaborate? I think this (in purely group theoretic terms with $k = \mathbb{Q}$) would give a desired counterexample, so I would be happy to accept it if you post an answer with more details. | |
| Nov 1, 2014 at 4:24 | comment | added | Derek Holt | I know nothing about group schemes, but if we were just talking about group extensions, then such an extension would not necessarily split as a direct product. For example if $k$ does not contain $4$-th roots of $1$ (e.g. $k = {\mathbb Q}$) and $m=2$, then an element outside of ${\rm GL}_n$ could centralize ${\rm GL}_n$ and square into $-I_n$. | |
| Nov 1, 2014 at 1:56 | history | asked | Kestutis Cesnavicius | CC BY-SA 3.0 |