$Designs from the groups $PSL_2(q)$ for certain $q

چکیده مقاله

Using primitive actions of the projective special linear groups $PSL_2(q)$, $q =$ 37, 41, 43, 47 and 49 some 1-designs are constructed. The automorphism group of all the constructed designs are found. It is shown that all subgroups of the automorphism group of $PSL_2(q)$, $q = $37, 41, 43, 47 and 49 appear as the automorphism group of the constructed designs.