Baer subgeometry partitions

For any odd integern 3 and prime powerq, it is known thatPG(n–1, q²) can be partitioned into pairwise disjoint subgeometries isomorphic toPG(n–1, q) by taking point orbits under an appropriate subgroup of a Singer cycle ofPG(n–1, q²). In this paper, we construct Baer subgeometry partitions of these spaces which do not arise in the classical manner. We further illustrate some of the connections between Baer subgeometry partitions and several other areas of combinatorial interest, most notably projective sets and flagtransitive translation planes.