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Results on the Projective Plane over a Finite Field of Order Seventeen

The main goal of this research is to find the projective mapping that transforms a geometric formation called an i -set onto an arc such that the domain of the mapping is a subset of the projective line PG (1,q), q=17 , such that a5-set is called a pentad, a6-set is a hexad, a7-set is a heptad, a8-set is an octad, and a9 -set is a nonad, mapped onto a conicY2-XZ. The research also aims to find the stabilizer group of points on a non-singular cubic curve, with or without rational inflection points, on the projective plane over a finite field of order seventeen, and to give some examples.