Projective Special Linear Group

The projective special linear group over a field is the quotient group of the special linear group by its group center,

(1)

Here is the identity matrix. It is also the image of in the projective general linear group and has a faithful group action on the projective space .

For the finite field , the group order of the group center is . Therefore, the group order of is

(2)

Here denotes the group order of a finite group . For , the group is a non-Abelian group and is simple, except for

			(3)
			(4)

In the notation of the Atlas of Finite Groups, the cases that are simple are also denoted .