Siegel transformations for even characteristic

Let V be a vector space over a field K of even characteristic and ∣K∣ > 3. Suppose K is perfect and π is an element in the special orthogonal group SO(V) with dim B(π)=2d. Then π = ρ1 ⋯ ρd−1κ, where ρj, j = 1 ,…, d − 1, are Siegel transformations and κ ∈ SO(V) with dim B(κ) = 2. The length of π with respect to the Siegel transformations is d if π is unipotent or if dim B (π)/rad B(π) ⩾ 4; otherwise it is d + 1.