Remark about a construction of some tournaments points of certain projective planes
Věroslav Jurák · Czech digital mathematics library · 1973
This paper present a study of the collineations on finite cyclic projective planes on N = n 2 + n + 1 points, where n is power of prime, these collineations being called collineations of period IV [1].It is shown, that for any finite projective plane there exist collineations, which have analogical properties as collineations of period N, so that we can say that these are collineations of a period smaller than N.All of these collineations of a given finite cyclic projective plane form a group, which is transitive on points and on lines of this plane or on subsets with points or lines of this plane; these collineations induce cycles of points of this plane.It is possible to construct a tournament with points of finite cyclic projective plane or tournament on vertices of regular iV-polygon.Hence we can say when regular AT-polygon breaks up or not to decomposition, i.e. when we can the circumference of /V-polygon draft by one closed way.Let <p be collineation of finite projective plane n over the Galois field GF(n), where n is power of prime, that <p(Po) = Pi, cp 2 (P 0 ) = cp(