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

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( ).

Highlights

Today, we see projective geometry as a numerical hypothesis in its own privilege, a section of geometry is “exceptionally non-Euclidean” with no thought of separation and with quite certain topological properties
The source of projective geometry is to be found inside Euclidean geometry
For a few hundreds of years, projective “techniques” were viewed as as an effective method to deal with issues in Euclidean geometry

Summary

Introduction

We see projective geometry as a numerical hypothesis in its own privilege, a section of geometry is “exceptionally non-Euclidean” with no thought of separation and with quite certain topological properties.

Results

Conclusion