Let $p$ be an odd prime. It is easy to show that $SL_2(3)$ can be embedded into $SL_2(p)$.
Now, let $n$ be an integer larger than $2$.
Question: In which circumstances, $SL_n(3)$ can be embedded into $SL_n(p)$?
Embedding $SL_n(3)$ into $SL_n(p)$
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