Special linear group (reviewed)

The special linear group $\SL(n,q)$ is the group of $n \times n$ matrices with determinant 1 with entries in the field $\F_q$ (the finite field with $q$ elements). It has order $|\GL(n, q)|/(q-1) = \frac{1}{q-1} \prod_{k=0}^{n-1} (q^n - q^k)$.

The projective special linear group $\PSL(n, q)$ is the quotient of $\SL(n, q)$ with the group of $n \times n$ scalar matrices over $\F_q$ with determinant 1. If either $n > 2$ or $q > 3$, then $\PSL(n, q)$ is a simple group.