Open AccessSplitting of PG(1,27) by Sets, Orbits, and Arcs on the Conic
Author(s) -
Emad Bakr Abdulkareem
Publication year - 2021
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2021.62.6.23
Subject(s) - conic section , line (geometry) , mathematics , plane (geometry) , pure mathematics , frame (networking) , matrix (chemical analysis) , order (exchange) , projective plane , geometry , combinatorics , field (mathematics) , computer science , chemistry , telecommunications , finance , chromatography , economics , correlation
This research aims to give a splitting structure of the projective line over the finite field of order twenty-seven that can be found depending on the factors of the line order. Also, the line was partitioned by orbits using the companion matrix. Finally, we showed the number of projectively inequivalent -arcs on the conic through the standard frame of the plane PG(1,27)