On the rank two geometries of the groups PSL (2, q): part I - Saedeleer, Julie De (Ars mathematica contemporanea, 2010)
We determine all firm and residually connected rank 2 geometries on which PSL?$(2,q)$? acts flag-transitively, residually weakly primitively and locally two-transitively, where one of the maximal parabolic subgroups is isomorphic to ?$E_q \colon \frac{(q - 1)}{(2, q - 1)}$?, where ?$E_q$? denotes an elementary abelian group of order ?$q$?, or ?$D_{2n(q)}$?, the dihedral group of order $2n(q)$ where ?$n(q) := \frac{(q ± 1)}{{\rm gcd}(2, q - 1)}$? for some prime-power ?$q$?.
Keywords: groupe; matematika