A Functional Equation with Biadditive Functions

Let S, H, X be groups. For two given biadditive functions A : S² → X, B : H² → X and for two unknown mappings T : S → H, g : S → S we will study the functional equation

B(T (x), T (y)) = A(x, g(y)), x, y ∈ S,

which is a generalization of the orthogonality equation in Hilbert spaces.