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Dec 19, 2011 at 1:13 comment added Geoff Robinson Thanks. Yes, the examples I mention are all examples where $G$ is solvable.
Dec 19, 2011 at 0:16 comment added Maurizio Monge Nice answer. And I should have known, as (if I remember correctly) the counterexamples pointed out occur as solvable subgroups of $GL(n,\mathbb{F}_q)$.
Dec 18, 2011 at 22:08 vote accept Maurizio Monge
Dec 18, 2011 at 22:08
Dec 18, 2011 at 11:20 history edited Geoff Robinson CC BY-SA 3.0
Minor typos
Dec 18, 2011 at 9:38 history answered Geoff Robinson CC BY-SA 3.0