The main goal of this thesis is a contribution to the classification of all incidence geometries<p>of rank two on which some group PSL(2,q), q a prime power, acts flag-transitively.<p>Actually we require that the action be RWPRI (residually weakly primitive) and (2T)1<p>(doubly transitive on every residue of rank one). In fact our definition of RWPRI requires<p>the geometry to be firm (each residue of rank one has at least two elements) and RC<p>(residually connected).<p><p>The main goal is achieved in this thesis.<p>It is stated in our "Main Theorem". The proof of this theorem requires more than 60pages.<p><p>Quite surprisingly, our proof in the direction of the main goal uses essentially the classification<p>of all subgroups of PSL(2,q), a famous result provided in Dickson’s book "Linear groups: With an exposition of the Galois field theory", section 260, in which the group is called Linear Fractional Group LF(n, pn).<p><p>Our proof requires to work with all ordered pairs of subgroups up to conjugacy.<p><p>The restrictions such as RWPRI and (2T)1 allow for a complete analysis.<p><p>The geometries obtained in our "Main Theorem" are bipartite graphs; and also locally 2-arc-transitive<p>graphs in the sense of Giudici, Li and Cheryl Praeger. These graphs are interesting in their own right because of<p>the numerous connections they have with other fields of mathematics. / Doctorat en Sciences / info:eu-repo/semantics/nonPublished