Flag-transitive and point-imprimitive symmetric designs with \(\lambda \leq 10\) (Q2120837)

A design \(D = (P, {\mathcal{B}}, I)\) be called flag-transitive design if there exists any automorphism group \(G\) of design \(D\), such that \(G\) acts transitively on the set of flags \(I\). Similarly, a design is called point-imprimitive if there exists any automorphism group \(G\), such that \(G\) acts imprimitively on the set of points \(P\). In this paper, the authors focus on flag-transitive and point-imprimitive symmetric designs with \(\lambda \leq 10\) and obtain some new results. If \((v, k, \lambda) \not\in \{(288, 42, 6), (891, 90, 9)\}\), then there are exactly eight nontrivial symmetric designs \(D\) with \(\lambda \leq 10\) admitting a flag-transitive and point-imprimitive subgroup of automorphisms.