engleski

Unitals, projective planes and other combinatorial structures constructed from the unitary groups U(3, q), q=3, 4, 5, 7

Let G be a finite permutation group acting primitively on sets Omega_1 and Omega_2. We describe a construction of a 1-design with the block set Omega_1 and the point set Omega_2, having G as an automorphism group. Applying this method, we construct a unital 2-(q^3+1, q+1, 1), and a semi-symmetric design (q^4-q^3+q^2, q^2-q, (1)) from the unitary group U(3, q), q=3, 4, 5, 7. From the unital and the semi-symmetric design we build a projective plane PG(2, q^2). Further, we describe other combinatorial structures constructed from these unitary groups.

block design; projective plane; unital; unitary group; primitive group

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