Timeline for What are immediate applications of the classification of connected reductive groups?
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| Sep 5, 2020 at 11:25 | comment | added | Mark Wildon | The latter, according to my understanding. (And I don't think this will be changed by any of the programmes to revise the proof of CFSG.) But I would defend my answer on the grounds that many useful structural properties of the finite groups do follow fairly immediately from the analogues in the algebraic group. E.g. existence of tori (and conjugation, although split/non-split tori in the finite case complicate things), $BN$ pairs, and the (related) Bruhat decomposition. | |
| Sep 4, 2020 at 22:39 | comment | added | Qiaochu Yuan | Is this really an application of the classification? In the following sense: does the proof of CSFG actually use the fact that we have an exhaustive list of reductive groups, or does it only use the constructions of the reductive groups without the fact that the classification is exhaustive? | |
| Sep 4, 2020 at 18:00 | history | edited | Mark Wildon | CC BY-SA 4.0 |
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| Sep 4, 2020 at 17:11 | history | answered | Mark Wildon | CC BY-SA 4.0 |