A Non PGL (3,q) k-arcs in the projective plane of order 37

Abstract

AbstractA k-arc in the plane PG(2,q) is a set of k points such that every line in the plane intersects it in at most two pointsand there is a line intersects it in exactly two points. The k-arc is complete if there is no k+1 -arc containing it.The main purpose of this paper is to study and find the projectively distinct k- arcs, k=4,5,6,7 in PG(2,37)through the classification and construction of the projectively distinct k-arcs and finding the group ofprojectivities of each projectively distinct k-arc and describing it. Also it was found that PG(2,37) has nomaximum arc .