Abstract
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.
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