Partitions on the Projective Plane Over Galois Field of Order 11^m, m=1, 2, 3

Sura M.A.  Al-subahawi; Najm Abdulzahra Makhrib  Al-seraji

doi:10.24996/ijs.2020.SI.1.28

Authors

Sura M.A. Al-subahawi Department of Mathematics, College of Science, University of Mustansiriyah, Baghdad, Iraq
Najm Abdulzahra Makhrib Al-seraji Department of Mathematics, College of Science, University of Mustansiriyah, Baghdad, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.SI.1.28

Keywords:

Stabilizer Group, Partitions, Arcs, Cross-Ratio

Abstract

This research is concerned with the study of the projective plane over a finite field . The main purpose is finding partitions of the projective line PG( ) and the projective plane PG( ) , in addition to embedding PG(1, ) into PG( ) and PG( ) into PG( ). Clearly, the orbits of PG( ) are found, along with the cross-ratio for each orbit. As for PG( ), 13 partitions were found on PG( ) each partition being classified in terms of the degree of its arc, length, its own code, as well as its error correcting. The last main aim is to classify the group actions on PG( ).