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Block designs and strongly regular graphs constructed from primitive groups

In [2] J. D. Key and J. Moori described a construction of symmetric 1-designs and regular graphs from primitive groups. Let G be a finite permutation group acting primitively on sets $\Omega_1$ and $\Omega_2$. Generalizing the method introduced in [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 (see [1]). Further, G acts primitively on points and blocks of the design. Applying this method, we construct 2-designs and strongly regular graphs from some classical groups. REFERENCES: [1] D. Crnković, V. Mikulić, Unitals, projective planes and other combinatorial structures constructed from the unitary groups U(3, q), q=3, 4, 5, 7, Ars Combin., to appear. [2] J. D. Key, J. Moori, Codes, Designs and Graphs from the Janko Groups $J_1$ and $J_2$, J. Combin. Math. Combin. Comput. 40 (2002), 143--159.

block design; strongly regular graph; linear group; unitary group; primitive group

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