On Jordan's theorem for complex linear groups

By M. J. Collins. 2007

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Finite subgroups of algebraic groups (2011, background): “Michael Collins determined the optimal values for J(n) [5] and J ′(n) [6].”
Product decompositions of quasirandom groups and a Jordan type theorem (2007, background): “o Blichfeldt: j(k) ≤ k! 6(k−1)π(k+1)+1 9 where π(k +1) denotes the number of primes ≤ k +1 (see [Do]). Better bounds can be obtained using CFSG. Building on an unpublished work of Weisfeiler, Collins [Co] has recently shown that for k ≥ 71 we have j(k) = (k +1)! (see [GL1] for the history of this re”
Jordan groups and automorphism groups of algebraic varieties (2013, background): “In particular, in [12] is proved that (a) the equality in (1) holds for all n > 71 and n D 63; 65; 67; 69; (b) JGLn.”