The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. PSU_n(q) is simple except for PSU_2(2) | = | S_3 PSU_2(3) | = | A_4 PSU_3(2) | = | 3^2 :Q_8, so it is given the simpler name U_n(q), with U_2(q) = L_2(q).
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