Dimensional linear spaces whose automorphism group is (line, hyperplane)- flag transitive (Q1182420)

Let \(S\) be a finite \(n\)-dimensional linear space with \(n\geq 4\) and moreover let \(G\) be an automorphism group of \(S\) acting transitively on the (line, hyperplane)-flags. In this work such pairs \((S,G)\) are classified and in particular it is proved that \(S\) must be either a Desarguesian projective or affine space provided with its superspaces of dimension \(\leq n-1\), or a Mathieu-Witt design provided with its blocks and its subsets of size \(\leq n-1\).