A characterization of the symplectic and unitary 3-transposition groups

Let D be a normal set of 3-transpositions in a group G. For each d ¿ D, let Dd be the set of elements e in D such that the order of de equals 2. Then we can define an equivalence relation ¿ on D by dre if and only if Dd d = De e. We characterize the symplectic and unitary groups over GF(2), respectively, GF(4) generated by their transvections as groups generated by a class D of 3-transposition with r trivial on D, but not when restricted to Dd for some d ¿ D.