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Let $n\ge 2$. Let $p$ be a prime and $\mathbb{Z}_p$ denote the finite field with $p$ elements.

I want to know about the presentation for the group $GL(n,\mathbb{Z}_p)$ consisting of its generators and the corresponding relations between them. It is known that $GL(2,\mathbb{Z}_2)\cong S_3$ and hence its generators and relations are those of $S_3$.

I have already asked a similar question here. But the relations between the generators have not been mentioned there.

Also, I have found a presentation for the group $GL(2,\mathbb{Z}_p)$ here but the relations between the generators seem incorrect.

Any help would be appreciated.

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    $\begingroup$ You say the relations between the generators for $\operatorname{GL}(2,p)$ were not given in your previous question, but this is not true. You were given a link to the book by Coxeter & Moser, which contains presentations for $\operatorname{GL}(2, p)$ for all primes $p$ on pp. 95-96. $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented 2 days ago
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    $\begingroup$ The relations given in the other question indeed seem wrong, but if you just follow the paper it links to (by Robertson & Williams) then you can easily find a presentation for $\operatorname{GL}(2,p)$ in there. Properly looking into all the information you've already been given is surely the bare minimum before you ask another question! $\endgroup$
    – Carl-Fredrik Nyberg Brodda
    Commented 2 days ago

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