# Special linear group is quasisimple

From Groupprops

## Statement

Let be a field and a natural number greater than . The special linear group is a quasisimple group: it is a perfect group and its inner automorphism group is a simple group, except in the following case: and has two or three elements.

In other words, if or has at least four elements, the special linear group is quasisimple.

## Facts used

## Proof

The proof follows from facts (1) and (2), and the fact that the inner automorphism group of the special linear group is the projective special linear group.