Transitive arcs in planes of even order (Q2563529)

In this paper, the author classifies all arcs in \(\mathrm{PG}(2,q)\), \(q\) even, which are stabilized by a transitive, irreducible (i.e., fixing neither a point nor any line) group \(G\), with the additional assumption that \(G\) does not stabilize a triangle in \(\mathrm{PG}(2,q)\) or in the extension \(\mathrm{PG}(2,q^3)\). The resulting list contains the unique hyperoval in a subplane \(\mathrm{PG}(2,4)\), certain 18-arcs among which the Lunelli-Sce hyperoval in a subplane \(\mathrm{PG}(2,16)\), and certain 36-arcs and 72-arcs, obtained by considering points on 1, 2 or 4 suitable cubic curves. The author also investigates the automorphism group of these arcs. His proofs make use of a computer.