Graphs with projective suborbits. Cases of small characteristics. I

This article is devoted to a positive solution, announced earlier by the author, of the question of boundedness of orders of stabilizers of vertices of connected finite symmetric graphs with projective suborbits. The case when the characteristic of the field is 3 and the automorphism group of the graph acts intransitively on its 3-arcs is considered. (The case when the characteristic of the field is 3 and the group acts transitively on the 3-arcs of the graph will be considered in Part II of this paper.) In parallel, some cases of a field of characteristic 2 are studied.