# Special linear group is quasisimple

Let $k$ be a field and $n$ a natural number greater than $1$. The special linear group $SL_n(k)$ is a quasisimple group: it is a perfect group and its inner automorphism group is a simple group, except in the following case: $n = 2$ and $k$ has two or three elements.
In other words, if $n \ge 3$ or $k$ has at least four elements, the special linear group $SL_n(k)$ is quasisimple.