Normal rational curves over prime fields (Q1364214)

A \(k\)-arc of \(PG(n,q)\), with \(k \geq n+1\), is set of \(k\) points of \(PG(n,q)\) such that no \(n+1\) of them belong to a hyperplane. Standard examples of \((q+1)\)-arcs of \(PG(n,q)\) are the normal rational curves. The author characterizes the normal rational curves in \(PG(n,p)\) for \(p\) prime and \(2 \leq n \leq p-2\) as the only \((p+1)\)-arcs admitting a projective group isomorphic to \(PSL(2,p)\). This result cannot be extended to proper primepowers since counterexamples are known to exist.