Timeline for Condition on $q$ for inclusion $p^{1+2r}\cdot\operatorname{Sp}(2r,p)\leqslant \operatorname{GU}(p^r,q)$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
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| Jul 17, 2023 at 7:48 | vote | accept | user488802 | ||
| Jul 14, 2023 at 23:57 | comment | added | Richard Lyons | Chastened, I've changed the answer to conform to ATLAS notation. | |
| Jul 14, 2023 at 22:52 | comment | added | Dave Benson | Now that I think about it, I suppose these notations probably come from page xx of the ATLAS. | |
| Jul 14, 2023 at 22:26 | comment | added | Dave Benson | @R.vanDobbendeBruyn The centre dot I've not come across, and I don't know its significance. From what I'm familiar with, an upper dot signifies a non-split extension, a colon indicates a split extension, and a lower dot indicates a lack of commitment as to whether it splits. The notation $p^{1+2r}$ usually indicates an extraspecial group of that order. | |
| Jul 14, 2023 at 21:30 | comment | added | R. van Dobben de Bruyn |
@DaveBenson I too was confused by the question, as I wrote in my earlier (now deleted) comments. And it seems so was the person who edited the lower dot to a middle dot (or does that notation occur as well?). A compromise I hope you can agree with is that I removed the algebraic-groups and finite-fields tags, since users who think about algebraic groups over finite fields (rather than the $\mathbf F_p$-points of these group schemes) are probably equally unaware that $p^{1+2r}$ means a group and not a number, that $G = N{.}H$ is a ternary relation on isomorphism types of groups, etcetera.
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| Jul 14, 2023 at 20:24 | comment | added | Dave Benson | Well, call me old-fashioned, but if one is unfamiliar with common finite group theory notation, maybe one shouldn't be voting to close a reasonable question on finite groups. I dunno, just a thought. | |
| Jul 14, 2023 at 18:53 | history | edited | R. van Dobben de Bruyn |
edited tags
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| Jul 14, 2023 at 17:21 | answer | added | Richard Lyons | timeline score: 7 | |
| Jul 14, 2023 at 13:18 | comment | added | Max Horn | The question is also clear to me, but to be fair there are different backgrounds and not everyone is familiar with the notational variants used in finite group theory... | |
| Jul 14, 2023 at 12:54 | history | edited | YCor | CC BY-SA 4.0 |
made title more specific
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| Jul 14, 2023 at 12:47 | comment | added | Dave Benson | It seems like a perfectly sensible question to me. For $p$ odd, the group $p^{1+2r}.\mathop{\rm Sp}(2r,p)$ is necessarily a split extension, and has an ordinary irreducible representation of degree $p^r$. The question is about its reduction modulo $q$ for a different prime $q$. I don't know why anyone would vote to close. | |
| Jul 14, 2023 at 12:39 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor formatting, grammar improvement and added a reference section
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| Jul 14, 2023 at 11:36 | review | Close votes | |||
| Jul 19, 2023 at 3:04 | |||||
| Jul 14, 2023 at 3:49 | history | asked | user488802 | CC BY-SA 4.0 |