Timeline for Maximal subgroups of simple groups with normal $2$-subgroups
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 12, 2018 at 11:08 | vote | accept | spin | ||
| Jan 29, 2018 at 16:50 | answer | added | Derek Holt | timeline score: 10 | |
| Jan 29, 2018 at 12:55 | comment | added | Geoff Robinson | Yes, using F-T is indeed not using the whole of CFSG, but I was using that example to illustrate the level of difficulty. In any case, I had deleted the comment. | |
| Jan 29, 2018 at 10:41 | comment | added | spin | @GeoffRobinson: Thank you for the comments. Perhaps one could make a trivial modification and assume that $G$ has even order, even though the question might remain very difficult. For "classification-free", I would say relying on Feit-Thompson is still classification-free, as long as there is no case-by-case checking of all finite simple groups. | |
| Jan 27, 2018 at 17:38 | comment | added | Geoff Robinson | As long as a simple group has a characteristic p BN-pair, ( and the Suzuki groups are examples where p=2 and the BN-pair has rank 1), I think things are OK. All overgroups of the Borel B are parabolic subgroups. There must be some maximal subgroup containing B-possibly B itself-and this must be a parabolic ( necessarily a maximal parabolic). Any such parabolic P has a non-trivial normal p-subgroup U, and then Z(U) is a non-trivial Abelian normal p-subgroup of P. | |
| Jan 26, 2018 at 20:49 | comment | added | YCor | Group of Lie type in char 2 include such groups as Suzuki groups for which the $SL_n$ intuition is possibly misleading. Is the notion of "maximal parabolic subgroup" well-defined and it is certain that they have a nontrivial abelian normal subgroup of 2-power order? | |
| Jan 26, 2018 at 14:55 | comment | added | Geoff Robinson | I think you have answered the second question yourself (allowing use of the classification): it only remains to check simple groups of Lie type in odd characteristic p, and then any maximal subgroup containing a Borel subgroup ( Sylow p- normalizer) works | |
| Jan 26, 2018 at 13:04 | history | asked | spin | CC BY-SA 3.0 |