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Galois theory, named after Évariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood.
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Variant of Hilbert 90 for Galois extensions
This is an application of Artin's Lemma to reduce to Hilbert 90. Namely, let $K$ be any field at all, and $G$ any finite subgroup of ${\rm{Aut}}(K)$ (as noted in this comments, such finiteness holds …