The Galois correspondence is a fundamental relationship between the field extensions and their corresponding Galois groups, providing a way to connect the structure of subfields with the subgroups of the Galois group. It illustrates how each intermediate field corresponds to a subgroup of the Galois group, allowing us to understand the roots of polynomials in terms of symmetries and automorphisms. This correspondence is particularly important in the context of splitting fields and normal extensions, as it helps us identify when a field extension is normal and how it relates to its Galois group.
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