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Could anyone help me with an example of a pair of generating elements for the group $\mathrm{PSL}(2,q)$?

Here $\mathrm{PSL}(2,q)$ denotes the group of $2\times 2$ matrices with determinant $1$ and whose entries are elements of a finite field of order $q$ (alternatively, the quotient group of $\mathrm{SL}(2,q)$ by its center).

Many thanks!

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    $\begingroup$ It's not a total duplicate, because $q$ was prime in the earlier question, and it's a prime power here. $\endgroup$
    – Derek Holt
    Commented Nov 25, 2013 at 14:59
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    $\begingroup$ Why has it been marked as a duplicate when it isn't? The previous answer doesn't say what the generators are even when $q$ is prime. $\endgroup$
    – Derek Holt
    Commented Nov 25, 2013 at 16:46

1 Answer 1

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The generators used by GAP (and Magma) are

$\left(\begin{array}{cc}w&0\\0&w^{-1}\end{array}\right)$, $\left(\begin{array}{cc}-1&1\\-1&0\end{array}\right),$

where $w$ is a primitive element of the field. The first generator has order $q-1$, and the second one order 3.

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