Timeline for Finite-maximal subgroups of orthogonal groups
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 23 at 13:43 | vote | accept | Andrea Aveni | ||
| Mar 19 at 11:41 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
clarifications
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| Mar 19 at 11:27 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
added thoughts on other finite maximal subgroups
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| Mar 17 at 19:42 | comment | added | Geoff Robinson | @YCor : Great. I think the statement in my answer about the hyperoctahedral group being maximal finite of maximal order will not be true in some small cases, (some larger than five, I think). | |
| Mar 17 at 19:01 | comment | added | YCor | @GeoffRobinson I have checked that it's maximal-finite for for all $n\ge 5$ (and thus it's not only for $n=2,4$). Details are a bit lengthy; these are mostly inequalities. No contradiction with $E_8$: the latter root system is invariant not under the full $\pm 1$-monomial group of order $2^8.8!$, but under its "'usual" index 2 subgroup. | |
| Mar 16 at 16:33 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
typo
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| Mar 16 at 16:12 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
clarified
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| Mar 16 at 13:36 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
clarification
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| Mar 16 at 13:11 | history | edited | Geoff Robinson | CC BY-SA 4.0 |
Roughly sketched justification of claim from Collins's Jordan's theorem result.
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| Mar 16 at 12:27 | comment | added | Geoff Robinson | It won't be unique, I think, but it will be of maximal possible order subject to being finite maximal in ${\rm O}_{n}(\mathbb{R})$ (for large enough $n$), and it will be unique one of that largest order. | |
| Mar 16 at 11:07 | comment | added | Andrea Aveni | Thank you, I found the article and it seems related (even though I don't quite yet see how to derive your claim from it). Do you think that the hyperoctahedral group is the unique finite-maximal subgroup of $\mathrm{O}_n(\mathbb R)$ for $n$ sufficiently large? | |
| Mar 16 at 10:53 | comment | added | Geoff Robinson | @YCor : Thanks, I had forgotten that question/answer. | |
| Mar 16 at 10:02 | comment | added | YCor | This is close to mathoverflow.net/questions/422947 | |
| Mar 16 at 8:22 | comment | added | YCor | I'd guess it's true for all $n\ge 5$. | |
| Mar 16 at 7:52 | history | answered | Geoff Robinson | CC BY-SA 4.0 |