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Let V be a form space. If W is a subspace of V we put W {ve Vl~(v, W) =0}. The form space V is called non-defective if V==0. It is called nondegenerate if dim(V=)< 1 and ~(v)#:0 for all non-zero wV  1.2. Assume that V is non-degenerate. V is defective if and only if char(k)=2 and e=0 and dim(V) is odd. If e= 1 then dim(V) is even. Let G = G(V) be the algebraic group in the sense of [-1] of the automorphisms geGl(V) which leave the forms fi and c~ invariant. Let g = g(V) be its Lie algebra. If e = 1 then G is the symplectic group Sp(V), so it is connected and semi-simple. If e=0 then G is the orthogonal group O(V), which is reductive. O(V) has two components if V is non-defective. O(V) is connected if V is defective. 1.3. Our object is to describe the conjugacy classes of the unipotent elements of G and of the nilpotent elements of g under the adjoint action of G given by

Nilpotency in classical groups over a field of characteristic 2