Timeline for Is the set of rational points of an (almost) simple algebraic group simple?
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Feb 28, 2023 at 9:24 | comment | added | Dave Benson | I think it's an example of the fact that there are only so many small simple groups, and some of them happen to coincide. Another example is that $U_4({\mathbb F}_2)$, $PSp_4({\mathbb F_3})$ and the derived group of $W(E_6)$ are all isomorphic. | |
| Feb 28, 2023 at 2:03 | comment | added | LSpice | @DaveBenson, is that just a fact of life, or is there some conceptual reason for it? (I don't know how conceptual I can hope for facts about $\mathsf G_2$ in characteristic $2$ to be, so it might be an unfair question!) | |
| Feb 28, 2023 at 0:36 | comment | added | Dave Benson | $G_2({\mathbb F}_2)$ has $U_3({\mathbb F}_3)$ as a subgroup of index two. | |
| Feb 27, 2023 at 22:55 | comment | added | paul garrett | Aha. "Ree groups". Keywords, forsooth! :) Thanks! :) | |
| Feb 27, 2023 at 22:54 | comment | added | LSpice | @paulgarrett, re, idle speculation, but perhaps it has something to do with Ree groups? But I'd expect that to give problems in characteristic $3$, not $2$ …. | |
| Feb 27, 2023 at 22:52 | history | edited | LSpice | CC BY-SA 4.0 |
What the parentheticals are indicating ($G$, not necessarily the image of $G(K)$)
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| Feb 27, 2023 at 22:41 | history | edited | LSpice | CC BY-SA 4.0 |
One more try!
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| Feb 27, 2023 at 22:34 | comment | added | LSpice | Oops, I originally wrote "adjoint" (despite getting it right in my comment), but @YCor's comment reminded me that that hardly ever works even in type $\mathsf A_1$. Fortunately, my error did not affect the type $\mathsf G_2$ that astonishes @paulgarrett. 😄 | |
| Feb 27, 2023 at 22:32 | history | edited | LSpice | CC BY-SA 4.0 |
Oops, simply connected, not adjoint
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| Feb 27, 2023 at 21:36 | comment | added | paul garrett | Wow, even including $G_2$ !?!?! :) | |
| Feb 27, 2023 at 21:27 | history | answered | LSpice | CC BY-SA 4.0 |