In that form, it states that there is a function ƒ(n) such that given a finite subgroup G of the group GL(n, C) of invertible n-by-n complex matrices, there is a subgroup H of G with the following properties: Schur proved a more general result that applies when G is not assumed to be finite, but just periodic.
Schur showed that ƒ(n) may be taken to be A tighter bound (for n ≥ 3) is due to Speiser, who showed that as long as G is finite, one can take where π(n) is the prime-counting function.
[1][2] This was subsequently improved by Hans Frederick Blichfeldt who replaced the 12 with a 6.
Unpublished work on the finite case was also done by Boris Weisfeiler.
when n is at least 71, and gave near complete descriptions of the behavior for smaller n.