Sublines and subplanes of PG(2,q3) in the Bruck–Bose representation in PG(6,q)

In this article we look at the Bruck–Bose representation of PG(2,q3) in PG(6,q). We look at sublines and subplanes of order q in PG(2,q3) and describe their representation in PG(6,q). We then show how these results can be generalized to the Bruck–Bose representation of PG(2,qn) in PG(2n,q).