Timeline for Lie Theory: Included in normalizer of a maximal Torus
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Sep 26, 2013 at 21:58 | answer | added | Little Lie Theory | timeline score: 0 | |
| Sep 25, 2013 at 16:24 | comment | added | Marguax | I should have added that the final sentence of the 2nd paragraph is false. The finite simple group $A_5$ has a 3-dimensional representation in characteristic 0 which can be "reduced mod $p$" to give a (faithful) representation into ${\rm{SL}}_3(k)$ for finite fields $k$ with sufficiently large characteristic $r$, thereby making $A_5$ an $r'$-subgroup. But the Weyl group of ${\rm{SL}}_3$ is $S_3$, so the $r'$-subgroup $A_5$ cannot lie inside the normalizer of any maximal torus. | |
| Sep 25, 2013 at 15:37 | answer | added | Jim Humphreys | timeline score: 1 | |
| Sep 25, 2013 at 14:07 | comment | added | Marguax | The condition that $K$ includes only semisimple elements is the same as the condition that the order of $K$ is prime to $r$, in view of the $\mathbf{F}_q$-rational Jordan decomposition and the existence of Sylow subgroups of finite groups. So the first sentence of your 3rd paragraph (phrased as a question) seems to be repeating the last sentence of your 2nd paragraph (not phrased as a question). Please clarify what you are asking for. | |
| S Sep 25, 2013 at 12:29 | history | suggested | Asaf | CC BY-SA 3.0 |
Latexed the mathematical expressions in the question
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| Sep 25, 2013 at 12:06 | review | Suggested edits | |||
| S Sep 25, 2013 at 12:29 | |||||
| Sep 25, 2013 at 10:27 | comment | added | José Figueroa-O'Farrill | You can use LaTeX on this site by simply surrounding the mathematical expressions with dollar signs! | |
| Sep 25, 2013 at 9:25 | review | First posts | |||
| Sep 25, 2013 at 9:25 | |||||
| Sep 25, 2013 at 9:06 | history | asked | Little Lie Theory | CC BY-SA 3.0 |