BASES NORMALES AUTODUALES ET GROUPES UNITAIRES EN CARACT ÉRISTIQUE 2

Let k be a field of characteristic 2, and let L/k be a finite Galois extension, with Galois group G. We show the equivalence of the following two properties: (∗) The group G is generated by elements of order 2 and by elements of odd order. (∗∗) There exists x ∈ L such that Tr(x) = 1 and Tr(x.g(x)) = 0 for every g ∈ G, g = 1.