Abstract
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.In addition, we shall endow the Baer geometry of order 2 with planes and show that the resulting geometry of rank 3 has the diagram:
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