The residually weakly primitive and locally two-transitive rank two geometries for the groups PSL(2, q)

• Main Author: De Saedeleer, Julie
• Other Authors: Buekenhout, Francis
• Format: Doctoral Thesis
• Language: fr
• Published: Universite Libre de Bruxelles 2010
• Subjects: Mathématiques; Sciences exactes et naturelles; Linear algebraic groups; Finite simple groups; Groupes linéaires algébriques; Groupes simples finis; locally s-arc-transitive graphs; Projective Special Linear Group; Coset Geometries
• Online Access: http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210037

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