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Sep 10, 2017 at 2:29 comment added Misha Just a historical note: The upper bound on the derived length in Part (2) of Yves' answer is due to H.Zassenhaus, 1938. (It follows from Malcev's theorem too, of course.)
Feb 5, 2016 at 1:36 comment added Misha Yves, this argument is indeed simpler than the one I originally had in mind. I was using Nori's theorem that for infinitely many finite fields $F_p$ the group $\Gamma$ maps to a subgroup between $G(F_p)$ and $G(F_p)^+$, where $G$ is the group scheme of the Zariski closure of $\Gamma$; provided that $\Gamma< GL(N, {\mathbb Q})$.
Feb 5, 2016 at 1:29 vote accept Misha
Feb 4, 2016 at 18:19 history answered YCor CC BY-SA 3.0