Embedding in the class of trigonometries of groups

We give a characterization of embeddability of one group trigonometry in another and argue that there exists an isomorphism between the trigonometries in question. A criterion for a group trigonometry to exist on a faithful pseudoplane is proved and a criterion for one trigonometry to be embeddable in another trigonometry on a projective plane is established.Translated fromAlgebra i Logika, Vol. 33, No. 4, pp. 429–447, July-August, 1994.Supported by the Russian Foundation for Fundamental Research, grant No. 93-011-1520.