On involutions of type O(q,k) over a field of characteristic two

In this article we study the involutions of O(V,q), an orthogonal group for a vector space V with quadratic form q over a field of characteristic two. The classification proceeds by discussing conjugacy classes of involutions arising as a product of transvections, involutions with respect to a hyperbolic space, and involutions acting nontrivially in the radical of V. We achieve a complete classification of the conjugacy classes of involutions when the quadratic space (V,q) is non-defective, and conclude with a discussion of the defective case.