Symmetric Designs With $\lambda =2$ Admitting $PSL(2,q)$ Fixing a Block

Abstract

It is shown that a symmetric design with $\lambda =2$ can admit $PSL(2,q)$ for $q$ odd and $q$ greater than $3$ as an automorphism group fixing a block and acting in its usual permutation representation on the points of the block only if $q$ is congruent to $5(\mathrm{mod}8)$. A consequence for more general automorphism groups is also described.