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By Jaroslav Jezek

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Theorem. Let D be a ternary ring. The projective plane P P (D) is (∞) − L∞ transitive if and only if the following are true: (1) D is reducible (2) D is a group with respect to + Proof. Let P P (D) be (∞) − L∞ transitive. Let a, m, b ∈ D. Put O = (0, 0), X = (0), Y = (∞), M = (m), Q = (1), R = (0, b), S = (a, T (a, m, b)), U = (Y ∨ S) ∧ (O ∨ M ), V = (X ∨ U ) ∧ (O ∨ Q), W = (V ∨ Y ) ∧ (R ∨ Q) (see Fig. 9). Denote by f the collineation with axis L∞ = X ∨ Y and center ∞ = Y , such that f (O) = R.

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