## Related pagesDesarguesian planes |

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.

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