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1, 545-551. [57c] Collineations and generalized incidence matrices. Trans. Amer. Math. Soc. 86, 284-296. Iden O. [01] On subplanes of free planes. Discrete Math. 241, 379-385. Kleinfeld E. [51] Alternative division rings of characteristic 2. Proc. Nat. Acad. Sci. USA 37, 818-820. [53] Right alternative rings. Proc. Amer. Math. Soc. 4, 939-944. Kopejkina L. I. (Golovina) [45] Svobodnye razlozheniya proektivnykh ploskostej. Izv. AN SSSR 9, 495-456. Mendelsohn E. 2] Every group is the colineation group of some projective plane.

Theorem. Let D be a ternary ring. The projective plane P P (D) is p-transitive for every line p containing (∞) if and only if D is a reducible ternary ring satisfying (1) D is an abelian group with respect to addition (2) (a + b)c = ac + bc for all a, b, c ∈ D (3) c(a + b) = ca + cb for all a, b, c ∈ D 30 3. COORDINATIZATION (4) for every a ∈ D − {0} there exists an element a−1 such that aa−1 = a−1 a = 1 and a−1 (ab) = b for all b ∈ D If these conditions are satisfied then (y(zy))x = y(z(yx)) for all x, y, z ∈ D.

56] Double transitivity in finite projective planes. Can. J. Math. 8, 563-567. Pickert G. [55] Projektive Ebenen. Springer. R. [97] Parallelisms of P G(3, 3) invariant under a collineation of order 5. In: N. L. ), Mostly finite geometries. Lecture Noters in Pure and Applied Mathematics 190, Marcel Dekker, 383-390. 42 BIBLIOGRAPHY [97a] Uniform parallelisms of P G(3, 3). In: Hirschfeld J. W. P. et al (eds), Geometry, combinatorial designs and related structures. LMS Lecture Notes 245, Cambridge University Press, 193-200.

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