Open AccessPartitions on the Projective Plane Over Galois Field of Order 11^m, m=1, 2, 3
Author(s) -
Sura M.A. Al-subahawi,
Najm Abdulzahra Makhrib Al-Seraji
Publication year - 2020
Publication title -
iraqi journal of science
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.152
H-Index - 4
eISSN - 2312-1637
pISSN - 0067-2904
DOI - 10.24996/ijs.2020.si.1.28
Subject(s) - projective plane , mathematics , blocking set , embedding , partition (number theory) , projective test , finite field , projective space , projective line , plane (geometry) , combinatorics , order (exchange) , pure mathematics , discrete mathematics , geometry , collineation , computer science , artificial intelligence , correlation , finance , economics
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( ).