INVARIANT RINGS OF ORTHOGONAL GROUPS OVER F2

We determine the rings of invariants S^G where S is the symmetric algebra on the dual of a vector space V over F2 and G is the orthogonal group preserving a non-singular quadratic form on V. The invariant ring is shown to have a presentation in which the difference between the number of generators and the number of relations is equal to the minimum possibility, namely dim V, and it is shown to be a complete intersection. In particular, the rings of invariants computed here are all Gorenstein and hence Cohen-Macaulay.