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Apr 29, 2015 at 10:27 comment added Derek Holt In fact ${\rm SL}(n,q^h)$ and ${\rm PGL}(n,q^h)$ are btoh simple groups in this case. I think it might be enough to have $n$ coprime to $(q^h-1)/(q-1)$.
Apr 29, 2015 at 9:37 history answered peliukas CC BY-SA 3.0