This might not be a well-informed question, but I started reading a bit about projective planes, and the following question occured to me:
Does Pappus's theorem hold in the Fano Plane?
Since the Fano Plane is the projective plane over $GF(2)$ which is commutative, then (if I understand correctly) it should be Pappian. But a Pappian configuration has 9 lines and 9 points, while the Fano Plane only has 7 lines and 7 points. So how could Pappus's theorem hold in the Fano Plane?