Let be a projective plane. Write . The elements of order 2 in have a very special structure. In fact, the following theorem holds.
Theorem. Let be an involutorial automorphism of . Then either has a center and an axis, or is a Baer subplane of .
In the latter case, the automorphism is called a Baer involution. An involutorial homology is also called a reflection. Unfortunately, there are also involutorial elations, in general.
Theorem. Let be a projective plane.