A Class of Partial Linear Spaces Related toPGL3(q2)

LetP=PG(2, q2).We shall define a geometry of rank 2-calledBaer geometry of order q-whose points are the Baer subplanes ofPand whose lines are the partitions ofPinto Baer subplanes induced by the Singer cycles ofP.The Baer geometry of orderqadmitsPGL3(q2)as a flag-transitive automorphism group. ition, we shall endow the Baer geometry of order 2 with planes and show that the resulting geometry of rank 3 has the diagram: