The projective special linear group PSL_n(q) is the group obtained from the special linear group SL_n(q) on factoring by the scalar matrices contained in that group. It is simple for n>=2 except for PSL_2(2) | = | S_3 PSL_2(3) | = | A_4, and is therefore also denoted L_n(Q).

projective special orthogonal group | projective special unitary group | special linear group