GRAPHS WITH PROJECTIVE SUBORBITS

Abstract

A positive answer is given to the problem of the existence of an upper bound for orders of stabilizers of vertices of connected graphs in vertex-transitive groups of automorphisms, if these stabilizers are finite and, under actions on adjacent vertices, contain the group PSLn(q) as normal subgroups in its natural doubly transitive representation, char Fq>3 (n and q fixed).