Timeline for What are the rank 3 boolean intervals [H,G], with G simple group?
Current License: CC BY-SA 4.0
16 events
| when toggle format | what | by | license | comment | |
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| Feb 4, 2023 at 6:09 | answer | added | Daniel Sebald | timeline score: 1 | |
| Aug 29, 2021 at 6:49 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
link to a recent paper
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| Aug 29, 2021 at 2:24 | comment | added | Richard Stanley | @Gro-Tsen: I don't see the difference between your two conditions. In any lattice $L$, a closed interval $[x,y]=\{ z\,:\, x\leq z\leq y\}$ is a sublattice of $L$. | |
| Aug 28, 2021 at 22:55 | answer | added | ahulpke | timeline score: 1 | |
| Aug 17, 2019 at 11:14 | comment | added | Sebastien Palcoux | @Gro-Tsen: yes! | |
| Aug 17, 2019 at 11:13 | comment | added | Gro-Tsen | So I think this means “yes” to all the extra conditions I listed. The way the question is written, it didn't seem clear (without the additional clarification you gave) that you are demanding lattice-equivalence with the lattice structure induced from the subgroup lattice and not just order-equivalence (or perhaps lattice-equivalence with a lattice structure that would come from the order but not the lattice of all subgroups). | |
| Aug 16, 2019 at 21:22 | comment | added | Sebastien Palcoux | @Gro-Tsen: we are looking for the classification of all the intervals $[H,G]$ in the subgroup lattice $\mathcal{L}(G)$ for all finite simple group $G$ such that $[H,G]$ is lattice-equivalent to the subset lattice of $\{1,2,3\}$ (i.e. the Boolean lattice of rank $3$). More generally, we are interested in such a classification for all rank $\ge 3$. Is it clearer? | |
| Aug 16, 2019 at 20:42 | comment | added | Gro-Tsen | Can you spell the question out completely? You are looking for $8$ groups $H_I$ one for each $I⊆\{1,2,3\}$, such that $H_J≤H_I$ whenever $J⊆I$, and with $G:=H_{\{1,2,3\}}$ simple? Or are there extra conditions like maybe $H_I∩H_J=H_{I∩J}$ and/or $\langle H_I∪H_J\rangle =H_{I∪J}$? Or that every subgroup between $H:=H_\varnothing$ and $G$ is one of the $H_I$? | |
| Aug 14, 2019 at 14:49 | answer | added | Sebastien Palcoux | timeline score: 0 | |
| Dec 15, 2018 at 16:33 | vote | accept | Sebastien Palcoux | ||
| May 22, 2018 at 3:37 | answer | added | John Shareshian | timeline score: 2 | |
| May 21, 2018 at 21:11 | history | edited | Sebastien Palcoux | CC BY-SA 4.0 |
class of examples: BN-pairs
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| Aug 1, 2016 at 3:57 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
typo edit on index
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| Jul 31, 2016 at 16:33 | comment | added | Sebastien Palcoux | We have used "SimpleGroupsIterator" and this code of A. Hulpke (he has found $A_8$ and $PSp(6,2)$ himself). | |
| Jul 31, 2016 at 16:32 | history | edited | Sebastien Palcoux | CC BY-SA 3.0 |
Addition of PSp(6,2) found by A. Hulpke.
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| Jul 26, 2016 at 2:29 | history | asked | Sebastien Palcoux | CC BY-SA 3.0 |