The projective symplectic group PSp_n(q) is the group obtained from the symplectic group Sp_n(q) on factoring by the scalar matrices contained in that group. PSp_(2m)(q) is simple except for Psp_2(2) | = | S_3 Psp_2(3) | = | A_4 Psp_4(2) | = | S_6, so it is given the simpler name S_(2m)(q), with S_2(q) = L_2(q).
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