Projective Special Linear Group

The projective special linear group ${\it PSL}_n(q)$ is the Group obtained from the Special Linear Group ${\it SL}_n(q)$ on factoring by the Scalar Matrices contained in that Group. It is Simple for $n\geq 2$ except for

$${\it PSL}_2(2) = S_3$$

$${\it PSL}_2(3) = A_4,$$

and is therefore also denoted $L_n(Q)$.

See also Projective Special Orthogonal Group, Projective Special Unitary Group, Special Linear Group

References

Conway, J. H.; Curtis, R. T.; Norton, S. P.; Parker, R. A.; and Wilson, R. A. ``The Groups ${\it GL}_n(q)$, ${\it SL}_n(q)$, ${\it PGL}_n(q)$, and ${\it PSL}_n(q)={\it L}_n(q)$.'' §2.1 in Atlas of Finite Groups: Maximal Subgroups and Ordinary Characters for Simple Groups. Oxford, England: Clarendon Press, p. x, 1985.