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In Derek Holt's answer to the question Generating pair for PSL(2,q)

He says that "the generators used by GAP (and Magma) are

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

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

Is there a formula for the order of $BA_w$ (in terms of $w$ and $q$)?

Though, I'd settle for a formula in $q$ that gives the order of $BA_w$ for some primitive element $w$ of $\mathbb{F}_q$.

Does anyone have references for this?

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  • The order of $BA_\omega$ depends on the choice of the primitive element $\omega$. I believe that the generators of the classical groups in GAP were computed by Don Taylor in Sydney, but I don't know whether he ever published anything. – Derek Holt Sep 17 '15 at 21:25
  • This is another non-sequitur, but could you please take a look at the comments that I posted here and here for me if you haven't already seen them? (You can delete this comment after you resolve it like you did the other one I sent you, too.) Anyway, thanks in advance. – RandomDSdevel Sep 24 '15 at 23:41

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