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YCor
YCor
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Embedding $SL_n$\mathrm{SL}_n(3)$ into $SL_n$\mathrm{SL}_n(p)$

Let$\DeclareMathOperator\SL{SL}$Let $p$ be an odd prime. It is easy to show that $SL_2(3)$$\SL_2(3)$ can be embedded into $SL_2(p)$$\SL_2(p)$.

Now, let $n$ be an integer larger than $2$.

Question: In which circumstances, $SL_n(3)$$\SL_n(3)$ can be embedded into $SL_n(p)$$\SL_n(p)$?

Embedding $SL_n(3)$ into $SL_n(p)$

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 $\mathrm{SL}_n(3)$ into $\mathrm{SL}_n(p)$

$\DeclareMathOperator\SL{SL}$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 $\SL_n(p)$?

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user44312
user44312
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Embedding $SL_n(3)$ into $SL_n(p)$

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 $SL_n(p)$?