Projective special linear group

Finite fields
Some facts:


 * For $$q = 2$$, $$PSL(n,q) = SL(n,q) = PGL(n,q) = GL(n,q)$$. For $$q$$ a power of two, $$PSL(n,q) = SL(n,q)$$ but this is not equal to $$GL(n,q)$$.
 * Projective special linear group equals alternating group in only finitely many cases: All those cases are listed in the table below.
 * Projective special linear group is simple except for finitely many cases, all of which are listed below.