engleski

Primitive designs constructed from simple groups

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. In particular, a simple group $G$ act primitively on a conjugacy class of a maximal subgroup and, therefore, we can construct $1-$designs from the group $G$. Applying this method, we construct simple block designs with parameters $(31, 6, 1)$, $(31, 6, 100)$, $(31, 10, 300)$, $(31, 15, 700)$, $(31, 3, 25)$, $(31, 12, 550)$ and $(31, 15, 875)$ from the group $L(3, 5)$. All constructed block designs have $L(3, 5)$ as the full automorphism group.

block design; linear group; primitive group

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