Related pages Desarguesian planes

A projective plane is a Moufang plane if each line is a translation axis.

We have the following important theorem.

Theorem. Let be a projective plane. The following statements are equivalent.

• is a Moufang plane.
• is (a,z)-transitive for all
• All (or one) ternary fields coordinatizing are alternative fields.
• All ternary fields coordinatizing are mutually isomorphic.
• The automorphism group of acts transitively on the set of all quadrangles.