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Homologies and elations of P(K,T)
A cartesian group is a linear ternary field with associative addition. In more concrete terms, a cartesian group consists of a set K and two operations such that the following axioms are satisfied.

Cartesian groups are characterized by the following geometrical property of there projective planes.

Theorem. A ternary field is a cartesian group if and only if the projective plane over (K,T) is - transitive.

In particular, the projective planes over cartesian groups are exactly the projective planes of Lenz type at least II.

See also

Contributed by Hauke Klein
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