Timeline for What are the rank 3 boolean intervals [H,G], with G simple group?

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Aug 17, 2019 at 3:37	comment	added	John Shareshian		It is quite reasonable to hope that, with more work than was required in the comment above, one can then show that $[H,G]$ is a Boolean algebra of rank $n-1$, thus rendering further computation unnecessary.
Aug 17, 2019 at 3:34	comment	added	John Shareshian		With respect to the remark: Let's work in $S_n$. It seems that $H$ is a Sylow $2$-subgroup. To prove this, first use the fact that a Sylow $2$-subgroup $H \leq S_{2^n}$ is an $n$-fold iterated wreath product of ${\mathbf Z}_2$ with itself to show by induction that this subgroup stabilizes an equipartition of each possible type and that these equipartitions have the desired refinement property. Then observe that a $2^n$-cycle stabilizes exactly one equipartition of each type. Then show by induction that no element of odd prime order stabilizes all equipartition stabilized by $H$......
Aug 16, 2019 at 19:48	history	edited	Sebastien Palcoux	CC BY-SA 4.0	Minor edit: same shutdown with S_{32}
Aug 14, 2019 at 17:16	history	edited	Sebastien Palcoux	CC BY-SA 4.0	Additional remark on the order of H
Aug 14, 2019 at 16:49	history	edited	Sebastien Palcoux	CC BY-SA 4.0	computation for S_{16}
Aug 14, 2019 at 14:49	history	answered	Sebastien Palcoux	CC BY-SA 4.0