Block designs constructed from the group U(3, 3) (CROSBI ID 106340)
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Crnković, Dean ; Mikulić, Vedrana ; Rukavina, Sanja
engleski
Block designs constructed from the group U(3, 3)
We show a construction of a symmetric (36, 15, 6) design and two symmetric (63, 31, 15) designs from the unitary group U(3, 3). Those designs are defined as incidence structures on the elements of the conjugacy classes of the maximal subgroups. Incidence matrices $M_i, \ i=1, 2, 3, $ of the constructed designs are symmetric matrices with 1 everywhere on the diagonal. Therefore, the matrices $M_i-I, \ i=1, 2, 3, $ are adjacency matrices of strongly regular graphs. Furthermore, we describe a construction of 2-(28, 12, 11), 2-(28, 4, 1) and 2-(36, 16, 12) designs from U(3, 3). The unitary group U(3, 3) acts transitively on the constructed designs and strongly regular graphs.
block design; symmetric design; unitary group; automorphism group; strongly regular graph
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