Automorphism of orthogonal groups in characteristic 2

Let V be a nondefective quadratic space over a field F of characteristic 2. Assume that V has dimension at least ten and that F has more than two elements. Let Δ be one of the groups O(V), O⁺(V), O′(V), or $\text{Ω(V)}$ (the full orthogonal group, the rotation group, the spinorial kernel, or the commutator subgroup of O(V), respectively). Then Λ is an automorphism of Λ if and only if Λ(σ) = gσg^?1 for all σ in Δ where g is a semilinear automorphism of V that preserves the quadratic structure of V in the sense that Q(gx) = αQ(x)^u for all x in V where Q is the quadratic form, α is some nonzero element of F, and u is the field automorphism of F associated to g.