Abstract

Let G be a finite group and let k be a field of char(k)≠2. We explicitly describe the set of trace forms of G-Galois algebras over k when the virtual 2-cohomological dimension vcd₂(k) of k is at most 1. For fields with vcd₂(k) ≤ 2 we give a cohomological criterion for the orthogonal sum of a trace form of a G-Galois algebra with itself to be isomorphic to another such form.

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