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The articles [R. Gramlich, C. Homan and S. Shpectorov. A Phan-type theorem for  Sp (2 n; q). J. Algebra  264  (2003), 358–384.] and [R. Gramlich. Weak Phan systems of type  C   n  .  J. Algebra  280  (2004), 1–19.] give a characterization of central quotients of the group Sp(2 n ,  q ) for  n  ≥ 3 and all prime powers  q , up to some small cases that are left open. The present article fills in this gap, thus providing the definitive version of the Phan-type theorem for Sp(2 n ,  q ).

The complete Phan-type theorem for Sp(2 n , q )