2021/12/29 by Alexander A. Davydov, Davydov, Alexander A., Stefano Marcugini +3
Engineering · Mathematics · #51E21 #51E22 #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2112.14803
openalex publication_date 2021/12/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the projective space PG(3,q), we consider the orbits of lines under the stabilizer group of the twisted cubic. In the literature, lines of PG(3,q) are partitioned into classes, each of which is a union of line orbits. In this paper, all classes of lines consisting of a unique orbit are found. For the remaining line types, with one exception, it is proved that they consist exactly of two or three orbits; sizes and structures of these orbits are determined. Also, the subgroups of the stabilizer group of the twisted cubic fixing lines of the orbits are obtained. Problems which remain open for one type of lines are formulated and, for 5≤ q≤37 and q=64, a solution is provided.