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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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Galois elements determined by action on $n$-th roots of rationals?

Can there be an element $\sigma$ of $Gal(\overline{\mathbb{Q}}/\mathbb{Q})$, other than the identity and complex conjugation, which is completely determined up to conjugacy by its action on $\sqrt[n]r …
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