The group action on the finite projective planes of orders 53, 61, 64
Najm Abdulzahra Makhrib Al-Seraji, Esam A. Alnussairy, Zainab Sadiq Jafar · Journal of Discrete Mathematical Sciences and Cryptography · 2020
The goal of this research is to partition the projective plane PG(2, q) over Galois Field of order q where q = 53, 61, 64. Classify the group action cyclic groups on PG(2, q), when the number of points and lines is equal to q2 + q + 1 which is not a prime have been described. Study the properties of the subsets (orbits, points, lines, planes, triangles) geometrically and algebraically. Also establish the projective codes and arcs with different sizes and degrees by using the program of GAP.