We shall be studying the following structure, which we shall call a V-form (“Vector-valued form”). Let G and W be additive abelian groups with every element of order 2 (i.e. vector spaces over the field GF(2) of two elements). Let there be given a symmetric bilinear map from G × G to W; we shall write it simply as a product ab. We define an equivalence relation on unordered n-ples of G. For n = 2: (a, b) ~ (c, d) if a + b = c + d and ab = cd. For n > 2 we define equivalence “piecewise”: there is to be a chain from (a 1, …, an ) to (b 1, …, bn ) where at each step only two elements are changed in accordance with the equivalence just defined for n = 2.