Flag-transitive point-quasiprimitive 2-\((v,\, k,\, 2)\) designs (Q1650808)

The main result of this paper is the following: Let \(\mathcal{D}\) be a 2-\((v,\, k,\, 2)\) design which admits a flag-transitive, point-quasiprimitive automorphism group \(G\). Then \(G\) is of holomorph affine or almost simple type. Another result asserts that if \(\mathcal{D}\) is a 2-\((v,\, k,\, 2\)) design which admits a flag-transitive automorphism group \(G\), then \(G\) is primitive if and only if it is quasiprimitive.