Automorphisms of unitary block designs
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In this paper, we discuss the geometry and determine the automorphism group of the unital or unitary block design associated with the threedimensional unitary group. If V is a three-dimensional vector space over the field with q2 elements and b is a non degenerate Hermitian bilinear form on V, we let X denote the family of isotropic one-dimensional subs paces of V with respect to b. Then X has 1 + q3 points, and the three-dimensional projective unitary groups, PSU(3, q) and PGU(3, q), act on X as doubly-transitive permutation groups. There is a naturally arising family of subsets of X, d, forming a unitary block design on X. Each member of d is the set of isotropic one-dimensional subs paces contained in a fixed nonisotropic two-dimensional subspace of V. Our principal result is:
[1] Michio Suzuki,et al. ON A CLASS OF DOUBLY TRANSITIVE GROUPS , 1962 .
[2] Ernest E. Shult,et al. On a class of doubly transitive groups , 1972 .
[3] Michio Suzuki. A characterization of the 3-dimensional projective unitary group over a finite field of odd characteristic , 1965 .