Timeline for Historical question concerning Jordan's theorem
Current License: CC BY-SA 2.5
5 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 3, 2010 at 17:40 | comment | added | Ben Green | Jim: I agree completely. I'd still like an actual reference to the argument I sketched above though, if there is one earlier than Tao's blog. | |
| May 3, 2010 at 17:10 | comment | added | Jim Humphreys | @Ben: The "simplest" argument that gives some bound may be one of those already mentioned, unless somebody finds a really new approach. Jordan's result is impressively general in scope, but the tools relevant to proving it seem quite limited. A more transparent proof would obviously be welcome. But after Frobenius and Schur, the published treatments (Curtis-Reiner, Isaacs,...) are basically similar apart from the way they are integrated with other theorems on finite groups and linear groups. Leaving aside the question of best bounds, it's hard to find a fresh approach. | |
| May 2, 2010 at 21:32 | comment | added | Ben Green | I should also point out that by $j(n)$ I think you mean the index of the biggest normal abelian subgroup of $A$; so your $j(n)$ is at most $F(n)!$, but they need not be the same. | |
| May 2, 2010 at 21:28 | comment | added | Ben Green | Igor, I believe this issue is comprehensively despatched in this paper of M. J. Collins: On Jordan's theorem for complex linear groups. J. Group Theory 10 (2007), no. 4, 411--423. He evaluates $j(n)$ for all $n$ and shows that $(n+1)!$ is the truth for $n \geq 71$ (and not for $n = 70$). But my interest is more in finding the simplest argument that gives some bound. | |
| May 2, 2010 at 21:18 | history | answered | Igor Pak | CC BY-SA 2.5 |