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.

- If is a Fano plane, then there does'nt exist an elation of order 2.
- If is an Antifano plane, then all elations of are involutorial.

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