ON CERTAIN CLASSES OF MAXIMAL SUBGROUPS IN PROJECTIVE SPECIAL UNITARY GROUPS OVER FINITE FIELDS

All maximal subgroups in PSU （n, q）(n≥3) containing T-subgroups are determined in thispaper, where a T-subgroup is meant the subgroup formed by all unitary transvections in a certaindirection. All the possible types of these maximal subgroups cover: the stabilizer of a totally iso-tropic subspace of the underlying space V, the stabilizer of a non-singular subspace of V of dimensionless than 1/2 dim V, the stabilizer of a decomposition of V into some mutually orthogonal non-singular subspaces of the same dimension （with a few exceptions）, PS（n,q） or PS（n, q） Z, embed-ded naturally in PSU（n, q） for even n, and a particular type for PSU（6,4）.