Permutation Group (psl (3, P), A <sub> 6 </ Sub>) Of The Track Structure

The orbits of the point stabilizer of a finite permutation group are called the suborbits of the permutation group. The determination of the suborbits of a permutation group is one of the basic problems in the permutation group theory. It plays an important role in the study of combinatorial structures. However, such a problem is very difficult in general, and it depends heavily on the understanding of abstract groups and the application of combinatorial tools as well. Recently, a lot of results have been apperaed dealing with the simple groups PSL(2,p). As for the simple groups PSL(3,p), such results are quite rare. In [14], Wang determined the suborbits of the primitive permutation representation of the simple groups PSL(3,p) relative to its maximal subgroups A₆ for p = 1(mod 180), but she did not deal with the paired suborbits of these suborbits. In this thesis, based on Wang's results, we shall almost determine the self-paired suborbits of these suborbits.