Geodesic
Congruence-Preserving Isomorphisms of the Translation Group associated with a Translation Plane
Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 214-221

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Let II, II′ be projective translation planes, their sets of points, l ∞, l ∞′ the improper lines, and T, T′ the corresponding translation groups. T is an Abelian group, simply transitive on . The set of the subgroups T s = {τ|τ∈ T, cen τ = S} for all S ∈ l∞ is called the congruence of II (cen τ = centre of τ). An injective map , where , is said to be a collineation of when and three points in are collinear if and only if their images are collinear; the set of these φ is denoted by and for we write 
Radó, F. Congruence-Preserving Isomorphisms of the Translation Group associated with a Translation Plane. Canadian journal of mathematics, Tome 23 (1971) no. 2, pp. 214-221. doi: 10.4153/CJM-1971-021-5
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